Solve the system using substitution. Check your answer.

Question

y = -2x+8
3y-x+4=0
(simplify your answer type integers or simplified fractions. type an ordered pair)

Answer 1

To solve the system using substitution, we need to isolate one of the variables in one of the equations and substitute it into the other equation.

Let's start by isolating y in the first equation:
y = -2x + 8

Now we can substitute this expression for y in the second equation:
3y - x + 4 = 0
3(-2x + 8) - x + 4 = 0
-6x + 24 - x + 4 = 0
-7x + 28 = 0
-7x = -28
x = -28 / -7
x = 4

Now that we have the value of x, we can substitute it back into the first equation to find y:
y = -2(4) + 8
y = -8 + 8
y = 0

Thus, the solution to the system is (4, 0).

To check our answer, let's substitute these values into both original equations:

First equation:
0 = -2(4) + 8
0 = -8 + 8
0 = 0 - correct!

Second equation:
3(0) - 4 + 4 = 0
0 - 4 + 4 = 0
0 = 0 - correct!

Therefore, the solution (4, 0) is correct.