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=(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=-(1)/(4) \end{gathered}`

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