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

(11, 13)

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)