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What is the value of \(x\)?
(1) \(6x + 12y = 36\)
(2) \(4y + 2x = 12\)
(1) \(6x + 12y = 36\)
(2) \(4y + 2x = 12\)
16 Sep 2014, 00:14
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Official Solution:
What is the value of \(x\)?
(1) \(6x + 12y = 36\)
One linear equation with two variables is not sufficient to find the value of \(x\).
(2) \(4y + 2x = 12\)
One linear equation with two variables is not sufficient to find the value of \(x\).
(1)+(2) Observe that by dividing the equation from (1) by 3, we get exactly the same equation as in (2). Hence, we still have only one equation with two variables, which is not sufficient to solve either for \(x\) or for \(y\).
Generally, if you have \(n\) distinct linear equations and \(n\) variables, then you can solve the system of equations for all the variables. "Distinct linear equations" means that no equation can be derived from the others through arithmetic operations such as multiplication or addition.
Answer: E
What is the value of \(x\)?
(1) \(6x + 12y = 36\)
One linear equation with two variables is not sufficient to find the value of \(x\).
(2) \(4y + 2x = 12\)
One linear equation with two variables is not sufficient to find the value of \(x\).
(1)+(2) Observe that by dividing the equation from (1) by 3, we get exactly the same equation as in (2). Hence, we still have only one equation with two variables, which is not sufficient to solve either for \(x\) or for \(y\).
Generally, if you have \(n\) distinct linear equations and \(n\) variables, then you can solve the system of equations for all the variables. "Distinct linear equations" means that no equation can be derived from the others through arithmetic operations such as multiplication or addition.
Answer: E
