8x - 3y = 18 (1)
4x + 5y = -4 (2)
Multiply equation (2) by (-2) (both sides). Keep equation (1) as is. You get an equivalent system
8x - 3y = 18 (1')
-8x - 10y = 8 (2')
Now add equations (1') and (2'). The terms "8x" will cancel each other, and you will get a single equation for the unique unknown y:
-3y + (-10y) = 18 + 8, or
-13y = 26. It implies y = = -2.
Next substitute the found value of y into equation (1). You will get
8x - 3*(-2) = 18 ====> 8x = 18 + 3*(-2) = 12 ====> x = = .
Answer. x = , y = -2.
Check the answer on your own.
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Notice that the standard and official name of this method is "the Elimination method".
