Question

Solve each system of equations by the substitution method.

3x + y = 19

2x – 5y = –10

Short answer

The solution of given system of equations is x = 5, y = 4.

Step-by-step solution

Step 1. Substitute value of one variable from one equation to another.

Add on both the sides of 3x + y = 19 and simplify.

3x + y – 3x = 19 – 3x

y = 19 – 3x

Substitute 19 – 3x for into 2x – 5y = – 10 and simplify.

2x – 5(19 – 3x) = –10

2x – 95 + 15 = –10

17x = 85

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 2 by 17 to find the value of x.

$\begin{array}{c}\frac{17x}{17}=\frac{85}{17}\\ x=5\end{array}$

Step 3. Solve for another variable.

Substitute 5 for x into 3x+ y= 19, to find the value of y.

$\begin{array}{c}3\times 5+y=19\\ 15+y=19\\ y=4\end{array}$

Therefore, the solution of given system of equations is x = 5, y = 4.