Question

Carolyn was asked to solve the following system of equations. Her work is shown. What is the solution to the system of linear equations?

Answer 1

Answer:

(11, 13)

Step-by-step explanation:

Carolyn's work is incorrect. Below is the correct solution:

Given:

$3x - 2y = 7$ ----› Equation 1

$y = x + 2$ -----› Equation 2

Substitute y = (x + 2) in equation 1

$3x - 2y = 7$ ----› Equation 1

$3x - 2(x + 2) = 7$ (substitution)

$3x - 2(x) -2(+2) = 7$ (distributive property)

[Note: this is where Carolyn made a mistake]

$3x - 2x - 4 = 7$

Collect like terms

$x - 4 = 7$

$x = 7 + 4$ (addition property of equality).

$x = 11$

Substitute x = 11 in equation 2

$y = x + 2$ -----› Equation 2

$y = 11 + 2$ (substitution)

$y = 13$

✅The solution to the system of equations would be:

(11, 13)