2x + y = 10 (1)
3x + 4y = 25 (2)
1. Eliminate y.
Method 1:
(1) x 4: 8x + 4y = 40 (1')
(1') - (2): 5x = 15
Method 2:
Rearrange (1): y = 10 - 2x (1")
Substitute (1") into (2): 3x + 4(10 - 2x) = 25 (3)
Expand (3): 3x + 40 - 8x = 25 (3")
Simplify (3"): 5x = 15
2. Find x.
5x = 15
=> x = 3
3. Substitute x into either (1) or (2).
e.g. Sub. into (1): 2(3) + y = 10
=> y = 4
4. Check your answer by substituting into the other equation (2) or (1).
e.g. Sub. into (2): LHS = 3x + 4y = 3(3) + 4(4) = 9 + 16 = 25 = RHS (note: if it does not equal the RHS, go back and find the mistake).
Solution: x = 3 and y = 4