Question

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

$\begin{array}{c}-6x+3y=33\\ -4x+y=16\end{array}$

Short answer

The solution is$x=-\frac{5}{2},y=6$.

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-:

$\begin{array}{c}-6x+3y=33\\ -4x+y=16\end{array}$

Multiplying the second equation by $3$and subtracting it from the first equation, we get

$\begin{array}{c}-6x+12x=33-48\\ 6x=-15\\ x=-\frac{5}{2}\end{array}$

Step-3 –Substituting the value of x in second equation, we get

$\begin{array}{c}-4x+y=16\\ -4\left(-\frac{5}{2}\right)+y=16\\ 10+y=16\\ y=16-10\\ y=6\end{array}$