\begin{aligned} 5x + 3y &= 22 \\ 3x + 5y &= 18 \end{aligned} If (x, y) is the solution to … — SAT

\begin{aligned} 5x + 3y &= 22 \\ 3x + 5y &= 18 \end{aligned}

If $(x, y)$ is the solution to the system of equations above, what is the value of $x - y$ ?

Answer: 2

The value of the expression

x - y

is 2.

Subtracting the second equation,

3x + 5y = 18

, from the first equation,

5x + 3y = 22

, yields

(5x - 3x) + (3y - 5y) = 22 - 18

, which simplifies to

2x - 2y = 4

. Dividing both sides of this equation by 2 isolates the expression

x - y

and yields a final value of 2.

Subtract the second equation from the first equation.

2x - 2y = 4

Subtracting the equations aligns the coefficients of

x

and

y

to form a multiple of the target expression

x - y

Divide both sides of the equation by 2.

x - y = 2

Dividing the expression

2x - 2y

by 2 isolates the target expression

x - y

Solving systems of linear equations by linear combination and algebraic manipulation.

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