Question

Solve each system of equation by graphing, substitution, or elimination.

$\begin{array}{c}-7x+6y=42\\ 3x+4y=28\end{array}$

Short answer

The solution is$x=0,y=7$.

Step-by-step solution

Step-1 – Concept of elimination

The process of adding or subtracting equation to remove a variable and simplify solving the system of equations is called elimination.

Step-2 – Using elimination to solve the equation

Given equations are-:

$\begin{array}{c}-7x+6y=42\\ 3x+4y=28\end{array}$

Multiplying the first equation by $3$and second equation by $7$and adding, we get

$\begin{array}{c}18y+28y=126+196\\ 46y=322\\ y=7\end{array}$

Step-3 – Substituting the value of y in first equation, we get

$\begin{array}{c}-7x+6y=42\\ -7x+6\left(7\right)=42\\ -7x+42=42\\ -7x=0\\ x=0\end{array}$