Question

Solve each system by the method of addition or subtraction.

$\mathbf{19}\mathbf{=}\mathbf{5}\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{y}$

$\mathbf{1}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{4}\mathbf{y}$

Short answer

The solution of given system of equations is $x=3$, $y=2$.

Step-by-step solution

Step 1. Description of step.

Multiply $19=5x+2y$by 2.

$2\times 19=2\left(5x+2y\right)$

$38=10x+4y$

Step 2. Description of step.

Add $38=10x+4y$and $1=3x-4y$and simplify.

$38+1=\left(10x+4y\right)+\left(3x-4y\right)$

$39=13x$

$13x=39$

Step 3. Description of step.

Divide each side of the equation obtained in step 2 by to find the value of x.

$\frac{13x}{13}=\frac{39}{13}$

$x=3$

Step 4. Description of step.

Substitute $3$for $x$into $1=3x-4y$and simplify.

$1=3\times 3-4y$

$1=9-4y$

$4y=8$

Step 5. Description of step.

Divide each side of the equation obtained in step 4 by to find the value of y.

$\frac{4y}{4}=\frac{8}{4}$

$y=2$

Therefore, the solution of given system of equations is $x=3$, $y=2$.