Question

Difficulty: EasySystems of Linear Equations

If the equations $x + 2y = 12$ and $x + y = 7$ are true for the same values of $x$ and $y$ , what is the value of $y$ ?

Answer: 5

The value of

y

is 5.

Subtracting the equation

x + y = 7

from

x + 2y = 12

gives

(x - x) + (2y - y) = 12 - 7

, which simplifies directly to

y = 5

Subtract the second equation from the first equation.

y = 5

Subtracting

x + y = 7

from

x + 2y = 12

eliminates the

x

terms, leaving a single linear equation in terms of

y

Solving systems of linear equations using elimination.

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