Maths-
SAT
Easy
Question
In the xy-plane, the equations x + 2y = 10 and 3x + 6y = c represent the same line for some constant c. What is the value of c ?
The correct answer is: 30
x + 2y = 10
subtract x from both sides
2y = 10 - x
divide both sides by 2
y = (10 - x) / 2 --------- eqn(1)
3x + 6y = c
subtract 3x from both sides
6y = c - 3x
divide both sides by 6
y = (c - 3x) / 6 ------- eqn(2)
eqn(1) = eqn(2)
(10 - x)/2 = (c - 3x)/6
6(10 - x) = 2(c - 3x)
60 - 6x = 2c - 6x
2c = 60 - 6x + 6x
2c = 60
c = 60/2
c = 30
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