If the pair (x, y) satisfies the system of linear equations below, what is the value of x … — GRE General Test

If the pair $(x, y)$ satisfies the system of linear equations below, what is the value of $x - y$ ?

\begin{aligned} 3x - 5y &= 14 \\ 2x + 7y &= -1 \end{aligned}

The value of

x - y

4

Solving the system of linear equations by elimination gives

x = 3

and

y = -1

. Substituting these values into the target expression

x - y

yields

3 - (-1) = 3 + 1 = 4

Eliminate one variable using the elimination method.

Multiply the first equation by

2

and the second equation by

3

6x - 10y = 28

6x + 21y = -3

Creating matching coefficients for

x

allows elimination of

x

by subtraction.

Subtract the first modified equation from the second modified equation to solve for

y

(6x + 21y) - (6x - 10y) = -3 - 28

31y = -31 \implies y = -1

Subtracting eliminates

x

, isolating

y

Substitute

y = -1

back into one of the original equations to solve for

x

3x - 5(-1) = 14 \implies 3x + 5 = 14 \implies 3x = 9 \implies x = 3

Plugging in

y

allows direct solution for

x

Evaluate the requested expression

x - y

x - y = 3 - (-1) = 3 + 1 = 4

Subtracting a negative value is equivalent to adding its positive value.

Solving systems of linear equations using elimination and evaluating algebraic expressions.

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