y = x -8 y= 5x

y = x -8 y= 5x

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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).

John R. | John R: Math, Science, and History TeacherJohn R: Math, Science, and History Teach...

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.

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