Q7.

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

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

Verified

Answer

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

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-:

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

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

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

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

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