Question

Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16 (1 point)
Responses

(2, 10)
left parenthesis 2 comma 10 right parenthesis

(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis

(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis

(2, 8)

Answer 1

To solve the system of equations using substitution, we can start by rearranging the first equation to solve for x:

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

Now substitute this expression for x into the second equation:

4x - 3y = -16
4((y - 2)/3) - 3y = -16
(4/3)(y - 2) - 3y = -16
(4/3)y - (8/3) - 3y = -16
(4/3)y - 3y - (8/3) = -16
(-(5/3)y - (8/3) = -16
-(5/3)y = -16 + (8/3)
-(5/3)y = -48/3 + 8/3
-(5/3)y = -40/3

Now, multiplying both sides of the equation by -3/5 to solve for y:

y = (-40/3) * (-3/5)
y = 40/5
y = 8

Substituting this value of y back into the first equation to solve for x:

x = (y - 2)/3
x = (8 - 2)/3
x = 6/3
x = 2

Therefore, the solution to the system of equations is (2, 8).