solve the following systems of linear equations by elimination, showing all work: -5y+9x=27 8y-x=-70
To do elimination, you need to make it so that one of the variable terms will cancel itself out. In other words, you need to be able to add two of one term together and get 0.
In this case, it's easiest to do that by making the x term in the second equation be -9x. So we mulitply that equation by 9. So now that equation is
72y - 9x = -630.
So now you can add the two equations together and you get
67y = -603
Divide both sides by 67 and you get y = -9.
Plug that back into the second equation to solve for x. Then you get
-72 - x = -70
-x = 2
x = -2
Eq(1)*8+Eq(2)*5 eliminates y : (-5y+9x)*8+(8y-x)*5 = 27*8-70*5 =-134. Or
(72-5)x = -134. Or 67x= -134/67 =-2.
Substituting x= -2 in eq(2) we get: 8y-(-2) = -70. Or
8y=-70-2 =-72. Or y = -72/8 =-9
We'll try to eliminate the unknown x and for this reason, we'll multiply the second equation with the value of 9 and , after that, we'll add the second equation to the first one.
-5y+9x + 9(8y-x)=27-9*70
-5y+9x + 72y-9x=27-630
After reducing similar terms, we'll have:
With the value for y,we'll go to the second equation and we'll substitute it, so that we'll obtain: