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MathHelper22
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.
<<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
\(\color{goldenrod}{ 14x-18y=4}\) [first equation] \(\color{cornflowerblue}{ -9x+18y=-12}\) [second equation] Adding the equations\[\color{goldenrod}{(14x-18y)}+\color{cornflowerblue}{(-9x+18y)}=\color{goldenrod}{(4)}+\color{cornflowerblue}{(12)}\]\[(\color{goldenrod}{14}-\color{cornflowerblue}{9})x+(\color{goldenrod}{-18}+\color{cornflowerblue}{18})y=\color{goldenrod}{4}+\color{cornflowerblue}{12}\]\[(\color{seagreen}5)x+(\color{seagreen}0)y=\color{seagreen}{16}\]\[\color{seagreen}5x=\color{seagreen}{16}\] \[x={\frac{\color{seagreen}{16}}{\color{seagreen}5}}\]