Chapter 6.2, Problem 5STP

Solve each exercise and enter your answer on the grid provided.

Solve the following system of equations using substitution. What is the value of $y$?

$\begin{array}{l}2x+3y=105\hfill \\ x+2y=65\hfill \end{array}$

To determine

To Solve: For the value of y.

Answer to Problem 5STP

The value of y is 25.

  

Explanation of Solution

Given information: $2x+3y=105$ and $x+2y=65$

Formula used: Substitution method to solve the system of equations.

Calculation:

Solve $x+2y=65$ for x then substitute it into the other equation.

Subtract both sides $2y$

  $x=65-2y$

Now, substitute $65-2y$ into the first equation for ‘ x’

  $2(65-2y)+3y=105$

Distribute to get rid the parentheses.

  $130-4y+3y=105$

Combine like terms,

  $130-1y=105$

Subtract both sides 130.

  $-1y=-25$

Divide both sides by -1.

  $y=25$

Hence the value of y is 25.