y = x -8 y= 5x
y = x -8 y= 5x
You can also use the method of elimination.
First, move all the terms with variables to one side of the equation.
y = x - 8 ==> y - x = x - 8 - x ==> y - x = -8
y = 5x ==> y - 5x = 5x - 5x ==> y - 5x = 0
Now, you want to add these two equations in a way that will eliminate one of the variables, which would leave you with the other variable to solve for.
So, (1) y - x = -8
(2) y - 5x = 0
Multiplying equation (2) by a -1 will give you a -y, which will be eliminated when added to equation (1).
That is:
(2) -1 * ( y - 5x = 0) ==> (-1)*y - (-1)*5x = (-1)*0 ==> -y - (-5x) = 0
==> -y + 5x = 0
Add this new equation to equation (1) above.
(1) y - x = -8
(2) -y + 5x = 0
+______________
0y + 4x = -8
4x = -8
(4x)/4 = (-8)/4
x = -2
Now that you have found x, plug into one of the original equations to find y.
(1) y = x - 8 ==> y = (-2) - 8 = -10
(2) y = 5x ==> y = 5*(-2) = -10
Thus, the solution for this system of equations is (-2, -10). You can check the answer by graphing these two linear equations on the same x,y-graph and finding the point at which they intersect, which should be (-2, -10).
The simplest method of solving this problem is the substitution method.
The reflexive property of equality states that any number (or variable) will equal itself, so we know that
y = y
We are now going to substitute the equivalent of y from each equation above to create a new equation.
x - 8 = 5x (The left side is the equivalent of y in the 1st equation. The right side is from the 2nd equation)
x - 8 -x = 5x -x (Subtract an x from each side)
-8 = 4x (Simplify)
-2 = x (Divide both sides by 4)
Now that we have the value of x, we can substitute the value of x into either equation to find the value of y.
y = x - 8 y = 5x
y = -2 - 8 y = 5 * (-2)
y = -10 y = -10
The solution to the problem is (-2, -10). That means x = -2 and y = - 10.