Question

solve the system of equations by the addition method3x - 4y = 78× + 12y = 13

Answer 1

We need to solve the following system:

$\mleft\{\begin{aligned}3x-4y=7 \\ 8x+12y=13\end{aligned}\mright.$

To do that we need to multiply the first equation by "3" and add both equations.

$\begin{gathered} \mleft\{\begin{aligned}9x-12y=21 \\ 8x+12y=13\end{aligned}\mright. \\ 9x+8x-12y+12y=21+13 \\ 17x=34 \\ x=\frac{34}{17} \\ x=2 \end{gathered}$

We can then replace the value of "x" we found above on one of the equations that form the system.

$\begin{gathered} 3\cdot2-4y=7 \\ 6-4y=7 \\ -4y=7-6 \\ -4y=1 \\ y=-\frac{1}{4} \end{gathered}$

The solution for this system is: x = 2 and y = -1/4.