Question

Solve the following system of equations by the substitution method: 8x = 2y + 5 and 3x = y + 7. What is the solution set?

A) {(-9/2, -41/2)}
B) {(-41/2, -9/2)}
C) {(9/2, 41/2)}
D) {(41/2, 9/2)}

Answer 1

To solve the system of equations by substitution method, solve one equation for one variable and substitute the expression into the other equation.

Step-by-step explanation:

To solve the system of equations by substitution method, we need to solve one equation for one variable and substitute that expression into the other equation.

Given the equations:

1) 8x = 2y + 5

2) 3x = y + 7

Solving equation 2) for y, we get y = 3x - 7. Now we substitute this expression into equation 1) as 8x = 2(3x - 7) + 5.

Simplifying this equation will give us the value of x. Then we substitute this value of x into equation 2) to find the value of y. The solution set is (-9/2, -41/2).