Problem: 5x+2y=22,x+3y=8
solve by elimination method
1) 5x + 2y = 22
2) x + 3y = 8
Multiply equation 2 by 5
5(x + 3y) = 8 * 5
3) 5x + 15y = 40
Subtract equation 1 from equation 3 to elimnate x
5x + 15y = 40
-(5x + 2y = 22)
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13y = 18
13y = 18
y = 18/13
Solve for x
2) x + 3y = 8
x + 3(18/13) = 8
x + 54/13 = 8
x + 54/13 - 54/13 = 8 - 54/13
x = 8 - 54/13
x = 104/13 - 54/13
x = 50/13
Check it.
1) 5x + 2y = 22
5(50/13) + 2(18/13) = 22
250/13 + 36/13 = 22
286/13 = 22
22 = 22
Answer: x = 50/13, y = 18/13