4x + 4y = 3 (1)
2x - 8y = -1 (2)
Multiply equation (1) by 2 (both sides). Keep equation (2) as is. You get an equivalent system
8x + 8y = 6 (1')
2x - 8y = -1 (2')
Now add equations (1') and (2'). The terms "8y" will cancel each other, and you will get a single equation for the unique unknown x:
8x + 2x = 6 + (-1), or
10x = 5. It implies x = = = 0.5.
Next substitute the found value of x into equation (1). You will get
4*0.5 + 4y = 3 ====> 4y = 3 - 4*0.5 = 1 ====> y = = 0.25.
Answer. x = 0.5, y = 0.25.
Check. 4*0.5 + 4*0.25 = 3 ! Correct !
2*0.5 - 8*0.25 = -1 ! Correct !
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Notice that the standard and official name of this method is "the Elimination method".
