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how to solve y = x -8 y=5x

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2 Answers

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.

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