Question

What is a possible first step to eliminate a variable in the following system?

7x - 9y = 2
3x - 6y = -4
Choices
Multiply the first equation by 2 and the second equation by -3.
Multiply the first equation by -3 and the second equation by -2.
Multiply the first equation by 7 and the second equation by 3.
Multiply the first equation by -2 and the second equation by 4.

Answer 1

A

Answer 2

Thanks man.

Answer 3

<<7x-9y=2

<<3x-6y=-4

When doing elimination the idea is to get one of the variables to cancel out.

2(7x-9y)=2(2) = 14x-18y=4 [first equation]

-3(3x-6y)=-3(-4) = -9x+18y=-12 [second equation]

You'll notice that the y's in this case cancel each other out.

Multiply the first equation by 2 and the second equation by -3

Answer 4

\(\color{goldenrod}{ 14x-18y=4}\) [first equation]

\(\color{cornflowerblue}{ -9x+18y=-12}\) [second equation]

Adding the equations\[\color{goldenrod}{(14x-18y)}+\color{cornflowerblue}{(-9x+18y)}=\color{goldenrod}{(4)}+\color{cornflowerblue}{(12)}\]\[(\color{goldenrod}{14}-\color{cornflowerblue}{9})x+(\color{goldenrod}{-18}+\color{cornflowerblue}{18})y=\color{goldenrod}{4}+\color{cornflowerblue}{12}\]\[(\color{seagreen}5)x+(\color{seagreen}0)y=\color{seagreen}{16}\]\[\color{seagreen}5x=\color{seagreen}{16}\]
\[x={\frac{\color{seagreen}{16}}{\color{seagreen}5}}\]