SOLUTION: Using the substitution method {x/8-y/5=1, x/6-y=5}

Question 280764: Using the substitution method {x/8-y/5=1, x/6-y=5}
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
Using the substitution method {x/8-y/5=1, x/6-y=5}

I would first get rid of the denominators. For the first equation, multiply everything by 40 (which I found by multiplying the denominator 8 by the denominator 5)

40 = 40
5x - 8y = 40 This is the new first equation.

I would get rid of the denominator 6 in the 2nd equation by multiplying everything by 6.

6 =6
x -6y = 30 This is the new second equation.

Here are the two equations now:

5x - 8y = 40
x -6y = 30 <----- now let's take this equation and solve for "x"

x - 6y = 30
x = 6y + 30 (added 6y to both sides to isolate the x)
Now that we know that "x" is equal to 6y + 30, let's "plug" that into the first equation.

5x - 8y = 40 First equation
5(6y + 30) -8y =40 Plugged in 6y + 30 for the "x" variable.
30y + 150 - 8y =40 Distributed 5 to 6y and 5 to 30.
22y + 150 = 40 Combined like terms: 30y - 8y = 22y
22y = 40 - 150 Subtracted 150 from both sides to begin to isolate the y
22y = -110 Found -110 by determining 40 - 150.
y = -5 Divided both sides by 22 to isolate the y. -110 divided by +22 equals -5.

Now we know that y = -5. Let's plug that into our 2nd equation.

x -6y = 30 Second equation
x -6(-5) = 30 Plugged -5 in for the "y" variable.
x + 30= 30 Determined 30 because -6 times -5 = 30
x = 30 - 30 Subtracted 30 from both sides to isolate the "x"
x = 0.

Now we have x = 0 and we have y = -5.

Let's check:

Original equations:

First original equation
Plug in the 0 for the X variable and -5 for the y variable.

This is correct. Yay.

Second original equation
Plug in 0 for the x variable and -5 for the y variable.

This is also correct. Yay.

We have proved the answers. I hope this helps you. :-)
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