Question

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

$\begin{array}{c}2y=5x-1\\ x+y=-1\end{array}$

Short answer

The solution is$x=-\frac{1}{7},y=-\frac{6}{7}$.

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-:

$\begin{array}{c}2y=5x-1\\ x+y=-1\end{array}$

Multiplying the second equation by $5$and adding with first equation, we get

$\begin{array}{c}2y+5y=-1-5\\ 7y=-6\\ y=-\frac{6}{7}\end{array}$

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

$\begin{array}{c}x+y=-1\\ x-\frac{6}{7}=-1\\ x=-1+\frac{6}{7}\\ x=-\frac{1}{7}\end{array}$