Linear equations in two variables (Day 5)
Solutions of practice sums
1) 148x + 231y = 527 — — —(1)
231x + 148y = 610 — — —(2)
Add equations (1) and (2)
148x + 231y = 527
231x + 148y = 610
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379x + 379y = 1137
[ Since all are divisible by 379]
Dividing throughout by 379
x + y = 3 — — —(3)
Subtract equation (1) from (2)
231x + 148y = 610
148x + 231y = 527
(-) (-) (-)
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83x — 83y = 83
Dividing throughout by 83
x — y = 1 — — —(4)
Add equations (3) and (4)
x + y = 3
x — y = 1
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2x = 4
x = 2
Substitute x = 2 in equation (3)
x + y = 3
2+ y = 3
y = 3–2
y = 1
Answer: x =2 and y = 1
2) 27x + 31y = 85 — — — (1)
31x + 27y = 89 — — — (2)
Add equations (1) and (2)
27x + 31y = 85
31x + 27y = 89
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58x + 58y = 174
Dividing throughout by 58
x + y = 3 — — —(3)
Subtract equations (1) from (2)
31x + 27y = 89
27x + 31y = 85
(-) (-) (-)
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4x — 4y = 4
Dividing throughout by 4
x — y = 1 — — —(4)
Add equations (3) and (4)
x + y = 3
x — y = 1
_________
2x = 4
x = 2
Substitute x = 2 in equation (3)
x + y = 3
2 + y = 3
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y = 3
Answer: x = 2 and y = 1
3) 2m + 3n = 27 — — — (1)
3m + 2n = 28 — — — (2)
Add equations (1) and (2)
2m + 3n = 27
3m + 2n = 28
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5m + 5n = 55
Dividing throughout by 55
m + n = 11 — — — (3)
Subtract equation (1) from (2)
3m + 2n = 28
2m + 3n = 27
(-) (-) (-)
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m — n = 1 — — — (4)
Add equations (3) and (4)
m + n = 11
m — n = 1
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2m = 12
m = 6
Substitute m = 6 in equation (3)
m + n = 11
6 + n = 11
n = 5
Answer: m = 6 and n = 5
