Q4.

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

$\begin{matrix} - 4 x + y = - 5 \\ 2 x + y = 7 \end{matrix}$

Verified

Answer

The solution is $x = 2, y = 3$ .

1Step-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.

2Step-2 – Using elimination to solve the equation

Given equations are-:

$\begin{matrix} - 4 x + y = - 5 \\ 2 x + y = 7 \end{matrix}$

Multiplying second equation by $2$ and adding, we get

$\begin{matrix} 3 y = - 5 + 14 \\ 3 y = 9 \\ y = 3 \end{matrix}$

Putting the value of $y$ in first equation, we get

$\begin{matrix} - 4 x + y = - 5 \\ - 4 x + 3 = - 5 \\ - 4 x = - 5 - 3 \\ - 4 x = - 8 \\ x = 2 \end{matrix}$