Question

Solve the system using substitution. 4 x equals 3 y minus 2. 18 equals 3 x plus y. (1 point) Responses the ordered pair (4, 6) Image with alt text: the ordered pair (4, 6) the ordered pair (2.5, 4) Image with alt text: the ordered pair (2.5, 4) the ordered pair (3, 9) Image with alt text: the ordered pair (3, 9) the ordered pair (3, negative 9)

Answer 1

To solve the system using substitution, we can start by solving the first equation for x:

4x = 3y - 2

Divide both sides by 4:
x = (3y - 2)/4

Now substitute this expression for x into the second equation:

18 = 3((3y - 2)/4) + y

Multiply 3 by (3y - 2)/4:
18 = (9y - 6)/4 + y

Multiply both sides by 4 to get rid of the fraction:
72 = 9y - 6 + 4y

Combine like terms:
72 = 13y - 6

Add 6 to both sides:
78 = 13y

Divide both sides by 13:
y = 6

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

4x = 3(6) - 2
4x = 18 - 2
4x = 16
x = 4

Therefore, the solution to the system of equations is the ordered pair (4, 6).