Question

Solve the system of equations and choose the correct answer from the list of options.

x + y = −3
y = 2x + 2

(5/3,4/3)
(-5/3, -4/)
(-3/5, -3/4)
(3/4, 3/5)

Answer 1

x = -5/3 ; y = -4/3   (-5/3, -4/3)

x + y = -3
y = 2x + 2

Substitute y in the 1st equation by its value in the 2nd equation.

x + 2x + 2 = -3
3x = -3 -2
3x = -5
x = -5/3

*substitute the value of x in the 1st equation to the 2nd equation to find the value of y.

y = 2x + 2
y = 2(-5/3) + 2
y = -10/3 + 2

In adding fractions, make sure that the denominators are the same. 
y = -10/3 + 2(3/3)
y = -10/3 + 6/3
y = (-10 + 6)/3
y = -4/3

Answer 2

x + y = −3 
y = 2x + 2

Plug in equation 2 into equation 1.

x + 2x + 2 = -3
3x + 2 = -3
3x = -5
x = -5/3

There is only one answer choice that has x = -5/3, and that is (-5/3, -4/3).

Just to be sure, let's find the y-value.

y = 2x + 2
y = 2(-5/3) + 2
y = -10/3 + 2
y = -10/3 + 6/3
y = (-10+6)/3
y = -4/3

Your answer is B. (-5/3, -4/3).