Problem: -7x + 4y = -6 and 2x - 5y = 21 mult with elimination method
need help!!
1) -7x + 4y = -6
2) 2x - 5y = 21
We eliminate one of the variables by multiplying one or both equations
by an appropriate constant in order to make the co-efficients of that
variable the same in both equations (or one positive and the other negative).
Then, we can subtract one equation from the other (or add the equations),
thereby eliminating the chosen variable. Numbering each equation makes it
easier to follow along.
Multiply equation 1 by 5.
5(-7x + 4y) = -6 * 5
3) -35x + 20y = -30
Multiply equation 2 by 4.
4(2x - 5y) = 21 * 4
4) 8x - 20y = 84
Add equation 4 to equation 3.
-35x + 20y = -30
8x - 20y = 84
----------------------
-27x = 54
-27x = 54
-27x/-27 = 54/-27
x = -2
Substitute that value into either of the original equation to solve for y.
-7x + 4y = -6
-7(-2) + 4y = -6
14 + 4y = -6
14 + 4y - 14 = -6 - 14
4y = -20
4y/4 = -20/4
y = -5
Substitute both of those values into the other given equation to verify your work.
-35x + 20y = -30
-35(-2) + 20(-5) = -30
70 + (-100) = -30
70 - 100 = -30
-30 = -30
If you made a mistake somewhere along the line, this second check will fail, telling
you that you need to go back and re-work the problem.
Answer: x = -2, y = -5