Question

Solve the following system of equations using the substitution method.

-X + 9y = -5
x - 5y = 1

Answer 1

Answer: x=8.5 y=1.5

Explanation:

Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.

-(5y+1) +9y =-5.

-5y-1+9y=-5.

-5y+9y= 1+5

4y= 6

Y=1.5

Now that you know what is the value of Y you can plug that into any equation.

5(1.5) +1

7.5+1

X=8.5

Answer 2

For this case we have the following system of equations:

`-x + 9y = -5\\x-5y = 1`

We clear "x" from the second equation and replace it in the first:

`x = 1 + 5y`

Substituting in the first equation:

`- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5`

We have similar terms:

`-1 + 4y = -5`

Adding 1 to both sides of the equation:

`4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1`

We look for the value of "x":

`x = 1 + 5 (-1)\\x = 1-5\\x = -4`

Answer:

`(x, y): (- 4, -1)`