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