Question 2753: I am studying for my 8th grade algebra final and i dont understand the way that on this linear system 4x+5y = 7
6x-2y = -18
how do i do this x = (7 -5y)/4
Substituting this expression into the second equation:
6(7+5y)/4-2y = -18
and from after that how do i simplify this 6(7+5y)/4-2y = -18
into this (-38)y = -114
I listen in class but i was absent on some very important days and this doesnt make sence
I thank anyone who could help.
Answer by WannabeCAgirl83(35)   (Show Source):
You can put this solution on YOUR website! You’re right. It doesn’t make sense that way because there are errors... ;-)
Your first aim is to bring x all alone on one side of the equation in order to find out what it equals, so that you can substitute x by its equivalent and thereby “get rid” of x as an unknown variable. Here’s how to do it:
4x + 5y = 7 | - 5y on both sides
4x = 7 - 5y | / 4 on both sides
x = 7/4 - 5/4y
As you found out that x is equal to 7/4 - 5/4y, you can substitute it in the next equation:
6x - 2y = -18
6(7/4 - 5/4y) - 2y = -18
Thereby you “got rid” of x and are now only dealing with one unknown variable (y) instead of two (x and y).
Your second aim is now to “get rid” of y the same way you “got rid” of x: You have to bring y all alone on one side of the equation to find out what it equals. Here’s how:
6(7/4 - 5/4y) - 2y = -18
10 ˝ - 7 ˝y - 2y = - 18
10 ˝ - 9 ˝ y = - 18 | - 10 ˝
- 9 ˝y = - 28 ˝ | / -9 ˝
y = 3
As you found out that y is equal to 3, you can substitute it in one of your equations in order to get a value for x:
4x + 5y = 7
4x +5(3) = 7
4x + 15 = 7 | - 15
4x = -8 | / 4
x = -2
Now you “got rid” of both of your unknown variables as you found out that:
x = -2 and y = 3
Let’s check if the values for x and y are correct by putting them in the original equations:
4x + 5y = 7
4(-2) + 5(3) = 7 → true
6x - 2y = - 18
6(-2) - 2(3) = - 18 → true
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