Q6.

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

$\begin{matrix} 3 x + 2 y = 18 \\ y = 6 x - 6 \end{matrix}$

Verified

Answer

The solution is $x = 2, y = 6$ .

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-:

$\begin{matrix} 3 x + 2 y = 18 \\ y = 6 x - 6 \end{matrix}$

Multiplying the first equation by $2$ and adding with second equation, we get

$\begin{matrix} 4 y + y = 36 - 6 \\ 5 y = 30 \\ y = 6 \end{matrix}$

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

$\begin{matrix} 3 x + 2 y = 18 \\ 3 x + 2 (6) = 18 \\ 3 x = 18 - 12 \\ 3 x = 6 \\ x = 2 \end{matrix}$