Question

Solve each system of equations by writing a new system that eliminates one of the variables.

Answer 1

Answer:

$x=2\\y=-1$

Step-by-step explanation:

Let:

$3x+2y=4\hspace{5}(1)\\and\\4x+7y=1\hspace{5}(2)$

We need to eliminate one of the variables, so let's use elimination method. First multiply (1) by 4 and (2) by 3:

$4*(1)\equiv\hspace{5}12x+8y=16\\3*(2)\equiv\hspace{5}12y+21y=3$

Now subtract 3*(2) from 4*(1) in order to eliminate x:

$4*(1)-3*(2)\\12x-12x+8y-21y=16-3\\-13y=13$

Solving for y:

Multiplying both sides by -1/13  

$y=-\frac{13}{13} =-1$

Finally, replacing the value of y in (1)

$3x+2*(-1)=4$

Solving for x:

add 2 to both sides:

$3x=6$

Multiply both sides by 1/3:

$x=\frac{6}{3} =2$