SOLUTION: how do i line up 7x - 4y = 8 with 4y = -7x + 9

Question 1067197: how do i line up 7x - 4y = 8 with 4y = -7x + 9
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is "line up?"
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
leve 7x - 4y = 8 alone.
with 4y = -7x + 9:
add 7x to both sides of the equation to get:
7x + 4y = 9

your two equations now line up if that's what i think you want.

the two equations are:

7x - 4y = 8
7x + 4y = 9

if you want to solve them simultaneously, you would add the second equation to the first equation to get:

14x = 17

you would solve for x to get x = 17/14.

when x = 17/14, 7x - 4y = 8 becomes 7*17/14 - 4y = 8, which becomes 4y = 119/14 - 8, which becomes 4y = 119/14 - 112/14 which becomes 4y = 7/14, which becomes y = 7/56.

when x = 17/14 and y = 7/56, both original equations are true.

that confirms the solution is correct.

for example:

7x + 4y = 9 becomes 7*17/14 + 4*7/56 = 9
this becomes 119/14 + 28/56 = 9
this becomes 119/14 + 7/14 = 9
this becomes 126/14 = 9
this becomes 9 = 9

an easieer way to check it is to just use your calculator.

7*17/14 + 4*7/56 = 9 becomes 9 = 9

using a scientific calculator, you would enter, in the following order:
7*17/14+4*7/56
you could also use parentheses if you wanted to make sure the arithmetic is done in the correct order as follows:
((7*17)/14)+((4*7)/56)
you'll get 9 either way.

when you add equations together, you add common terms on each side of the equation.

7x + 7x = 14x
-4y + 4y = 0
8 + 9 = 17

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