Solving Linear Equations, with 3 unknowns
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0
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$$6x-8y=24$$
$$frac{-2}{3}x+ frac{8}{9}y = m$$
I want to solve for all three of the variables. I did plot this into my calculator and the answer is $$frac{-8}{3}$$ I want to know the process in solving it.
linear-algebra fractions
asked Dec 5 at 12:03
Mattking32
11
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up vote
0
down vote
favorite
$$6x-8y=24$$
$$frac{-2}{3}x+ frac{8}{9}y = m$$
I want to solve for all three of the variables. I did plot this into my calculator and the answer is $$frac{-8}{3}$$ I want to know the process in solving it.
linear-algebra fractions
asked Dec 5 at 12:03
Mattking32
11
4
Two linear equations will not determine $3$ unknowns uniquely. Furthermore, how is "$-frac{8}{3}$" an answer when asking for the values of $3$ unknowns?
– Christoph
Dec 5 at 12:07
Do u know Gaussian elimination?
– Cloud JR
Dec 5 at 12:07
@christoph well asked lol
– Cloud JR
Dec 5 at 12:08
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
$$6x-8y=24$$
$$frac{-2}{3}x+ frac{8}{9}y = m$$
I want to solve for all three of the variables. I did plot this into my calculator and the answer is $$frac{-8}{3}$$ I want to know the process in solving it.
linear-algebra fractions
asked Dec 5 at 12:03
Mattking32
11
$$6x-8y=24$$
$$frac{-2}{3}x+ frac{8}{9}y = m$$
I want to solve for all three of the variables. I did plot this into my calculator and the answer is $$frac{-8}{3}$$ I want to know the process in solving it.
linear-algebra fractions
linear-algebra fractions
asked Dec 5 at 12:03
Mattking32
11
asked Dec 5 at 12:03
Mattking32
11
asked Dec 5 at 12:03
Mattking32
11
asked Dec 5 at 12:03
Mattking32
11
asked Dec 5 at 12:03
Mattking32
11
11
4
Two linear equations will not determine $3$ unknowns uniquely. Furthermore, how is "$-frac{8}{3}$" an answer when asking for the values of $3$ unknowns?
– Christoph
Dec 5 at 12:07
Do u know Gaussian elimination?
– Cloud JR
Dec 5 at 12:07
@christoph well asked lol
– Cloud JR
Dec 5 at 12:08
add a comment |
4
Two linear equations will not determine $3$ unknowns uniquely. Furthermore, how is "$-frac{8}{3}$" an answer when asking for the values of $3$ unknowns?
– Christoph
Dec 5 at 12:07
Do u know Gaussian elimination?
– Cloud JR
Dec 5 at 12:07
@christoph well asked lol
– Cloud JR
Dec 5 at 12:08
4
4
Two linear equations will not determine $3$ unknowns uniquely. Furthermore, how is "$-frac{8}{3}$" an answer when asking for the values of $3$ unknowns?
– Christoph
Dec 5 at 12:07
Two linear equations will not determine $3$ unknowns uniquely. Furthermore, how is "$-frac{8}{3}$" an answer when asking for the values of $3$ unknowns?
– Christoph
Dec 5 at 12:07
Do u know Gaussian elimination?
– Cloud JR
Dec 5 at 12:07
Do u know Gaussian elimination?
– Cloud JR
Dec 5 at 12:07
@christoph well asked lol
– Cloud JR
Dec 5 at 12:08
@christoph well asked lol
– Cloud JR
Dec 5 at 12:08
add a comment |
2 Answers
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1
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Since you has three unknowns, you need three equations to be able to solve for all three variables (your system of linear equations is underdetermined).
However, what you can do is solve for $m$.
Multiplying the second equation through by $-9$ we get:
$$ 6x - 8y = -9m$$
Aha! This looks a lot like our first equation: we already know $6x - 8y = 24$. Putting these together gives $-9m = 24$ and hence $$m = -frac{8}{3}$$
However, without another equation we cannot determine $x$ and $y$ (for example, both $x = 0, y=-3$ and $x = 4, y=0$ satisfy your system of equations. In fact, there will be infinitely many values of $x$ and $y$ satisfying the two equations).
answered Dec 5 at 12:09
ODF
78438
add a comment |
up vote
1
down vote
From $frac{-2}{3}x+ frac{8}{9}y = m$ we get $-6x+8y=9m$. If we add this to the first equation we get $24+9m=0$, hence $m=frac{-8}{3}.$
It remains only one equation: $ 6x-8y=24$. There are infinitely many pairs $(x,y)$ which are solutions of this equation.
answered Dec 5 at 12:09
Fred
43.8k1644
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Since you has three unknowns, you need three equations to be able to solve for all three variables (your system of linear equations is underdetermined).
However, what you can do is solve for $m$.
Multiplying the second equation through by $-9$ we get:
$$ 6x - 8y = -9m$$
Aha! This looks a lot like our first equation: we already know $6x - 8y = 24$. Putting these together gives $-9m = 24$ and hence $$m = -frac{8}{3}$$
However, without another equation we cannot determine $x$ and $y$ (for example, both $x = 0, y=-3$ and $x = 4, y=0$ satisfy your system of equations. In fact, there will be infinitely many values of $x$ and $y$ satisfying the two equations).
answered Dec 5 at 12:09
ODF
78438
add a comment |
up vote
1
down vote
Since you has three unknowns, you need three equations to be able to solve for all three variables (your system of linear equations is underdetermined).
However, what you can do is solve for $m$.
Multiplying the second equation through by $-9$ we get:
$$ 6x - 8y = -9m$$
Aha! This looks a lot like our first equation: we already know $6x - 8y = 24$. Putting these together gives $-9m = 24$ and hence $$m = -frac{8}{3}$$
However, without another equation we cannot determine $x$ and $y$ (for example, both $x = 0, y=-3$ and $x = 4, y=0$ satisfy your system of equations. In fact, there will be infinitely many values of $x$ and $y$ satisfying the two equations).
answered Dec 5 at 12:09
ODF
78438
add a comment |
up vote
1
down vote
up vote
1
down vote
Since you has three unknowns, you need three equations to be able to solve for all three variables (your system of linear equations is underdetermined).
However, what you can do is solve for $m$.
Multiplying the second equation through by $-9$ we get:
$$ 6x - 8y = -9m$$
Aha! This looks a lot like our first equation: we already know $6x - 8y = 24$. Putting these together gives $-9m = 24$ and hence $$m = -frac{8}{3}$$
However, without another equation we cannot determine $x$ and $y$ (for example, both $x = 0, y=-3$ and $x = 4, y=0$ satisfy your system of equations. In fact, there will be infinitely many values of $x$ and $y$ satisfying the two equations).
answered Dec 5 at 12:09
ODF
78438
Since you has three unknowns, you need three equations to be able to solve for all three variables (your system of linear equations is underdetermined).
However, what you can do is solve for $m$.
Multiplying the second equation through by $-9$ we get:
$$ 6x - 8y = -9m$$
Aha! This looks a lot like our first equation: we already know $6x - 8y = 24$. Putting these together gives $-9m = 24$ and hence $$m = -frac{8}{3}$$
However, without another equation we cannot determine $x$ and $y$ (for example, both $x = 0, y=-3$ and $x = 4, y=0$ satisfy your system of equations. In fact, there will be infinitely many values of $x$ and $y$ satisfying the two equations).
answered Dec 5 at 12:09
ODF
78438
answered Dec 5 at 12:09
ODF
78438
answered Dec 5 at 12:09
ODF
78438
answered Dec 5 at 12:09
ODF
78438
78438
add a comment |
add a comment |
up vote
1
down vote
From $frac{-2}{3}x+ frac{8}{9}y = m$ we get $-6x+8y=9m$. If we add this to the first equation we get $24+9m=0$, hence $m=frac{-8}{3}.$
It remains only one equation: $ 6x-8y=24$. There are infinitely many pairs $(x,y)$ which are solutions of this equation.
answered Dec 5 at 12:09
Fred
43.8k1644
add a comment |
up vote
1
down vote
From $frac{-2}{3}x+ frac{8}{9}y = m$ we get $-6x+8y=9m$. If we add this to the first equation we get $24+9m=0$, hence $m=frac{-8}{3}.$
It remains only one equation: $ 6x-8y=24$. There are infinitely many pairs $(x,y)$ which are solutions of this equation.
answered Dec 5 at 12:09
Fred
43.8k1644
add a comment |
up vote
1
down vote
up vote
1
down vote
From $frac{-2}{3}x+ frac{8}{9}y = m$ we get $-6x+8y=9m$. If we add this to the first equation we get $24+9m=0$, hence $m=frac{-8}{3}.$
It remains only one equation: $ 6x-8y=24$. There are infinitely many pairs $(x,y)$ which are solutions of this equation.
answered Dec 5 at 12:09
Fred
43.8k1644
From $frac{-2}{3}x+ frac{8}{9}y = m$ we get $-6x+8y=9m$. If we add this to the first equation we get $24+9m=0$, hence $m=frac{-8}{3}.$
It remains only one equation: $ 6x-8y=24$. There are infinitely many pairs $(x,y)$ which are solutions of this equation.
answered Dec 5 at 12:09
Fred
43.8k1644
answered Dec 5 at 12:09
Fred
43.8k1644
answered Dec 5 at 12:09
Fred
43.8k1644
answered Dec 5 at 12:09
Fred
43.8k1644
43.8k1644
add a comment |
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4
Two linear equations will not determine $3$ unknowns uniquely. Furthermore, how is "$-frac{8}{3}$" an answer when asking for the values of $3$ unknowns?
– Christoph
Dec 5 at 12:07
Do u know Gaussian elimination?
– Cloud JR
Dec 5 at 12:07
@christoph well asked lol
– Cloud JR
Dec 5 at 12:08