Solve the system of two equations using subtraction y equals 2 + 3x and 4x- 3y = -16

Answer 1

To solve the system of equations using subtraction, we'll eliminate one variable by multiplying one of the equations by a constant so the coefficients of that variable are opposite in sign.

1) y = 2 + 3x
2) 4x - 3y = -16

Let's multiply equation (1) by 3 to make the coefficients of y opposite:
3 * (y) = 3 * (2 + 3x)
3y = 6 + 9x

Now our new system of equations is:
3) 3y = 6 + 9x
4) 4x - 3y = -16

Now we can subtract equation (3) from equation (4) to eliminate the y variable:
(4x) - (3y) - (4x) + (3y) = (-16) - (6 + 9x)
0 = -16 - 6 - 9x
0 = -22 - 9x

Let's solve for x:
9x = -22
x = -22/9

Now substitute this value of x back into equation (1) or (2) to find y. Let's use equation (1):
y = 2 + 3(-22/9)
y = 2 - 66/9
y = 2 - 22/3
y = (6/3) - (22/3)
y = -16/3

Therefore, the solution to the system of equations is x = -22/9 and y = -16/3.