Question

Solve each system by the method of addition or subtraction.

$\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{1}$

$\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{21}$

Short answer

The solution of given system of equations is $x=11$, $y=16$.

Step-by-step solution

Step 1. Description of step.

Subtract $2y=x+21$from $2y=3x-1$and simplify.

$2y-2y=\left(3x-1\right)-\left(x+21\right)$

$0=2x-22$

$2x=22$

Step 2. Description of step.

Divide each side of the equation obtained in step 1 by to find the value of x.

$\frac{2x}{2}=\frac{22}{2}$

$x=11$

Step 3. Description of step.

Substitute for into $2y=3x-1$and simplify.

$2y=3\times 11-1$

Step 4. Description of step.

Divide each side of the equation obtained in step 3 by to find the value of y.

$\frac{2y}{2}=\frac{32}{2}$

$y=16$

Therefore, the solution of given system of equations is $x=11$, $y=16$.