Question

Use the substitution method to find the solution for the system of equations. Write the answer as an ordered pair. 3x + 2y = 23

1/2 x - y = 4

Answer 1

The solution to the system of equations using the substitution method is the ordered pair (31/4, -1/8), found by solving one of the equations for y and substituting it into the other.

Step-by-step explanation:

To solve the system of equations using the substitution method, we first need to solve one of the equations for either x or y, and then substitute that expression into the other equation to find the value of the other variable. We are given the equations 3x + 2y = 23 and 1/2x - y = 4.

Step-by-Step Solution

1. Solve the second equation for y: y = 1/2x - 4.

Substitute this expression for y into the first equation: 3x + 2(1/2x - 4) = 23.Simplify and solve for x: 3x + x - 8 = 23 -> 4x = 31 -> x = 31/4.Substitute x back into the expression for y: y = 1/2(31/4) - 4.Solve for y: y = 31/8 - 32/8 -> y = -1/8.

1. The solution as an ordered pair is therefore (31/4, -1/8).