Question

Solve the following system of equations using elimination. 2x + 5y = 12 -2x + 3y = 4

Answer 1

$\begin{gathered} 2x+5y=12 \\ -2x+3y=4 \end{gathered}$

To solve a system of equation using elimination:

1. If it is necesary multyiply one of both equations for a number that makes each equation have an opposite term to the other equation.

In this case the equations already have opposite terms (2x and -2x)

2. Add equations:

3. Solve the variable in the result of substraction:

$\begin{gathered} 8y=16 \\ y=\frac{16}{8} \\ \\ y=2 \end{gathered}$

4. Use the value of the variable you get in the previus step to solve the other variable:

$\begin{gathered} 2x+5y=12 \\ y=2 \\ \\ 2x+5(2)=12 \\ 2x+10=12 \\ 2x=12-10 \\ 2x=2 \\ x=\frac{2}{2} \\ \\ x=1 \end{gathered}$Then, the solution for the system of equations is x=1 and y=2