Consider the system of equations below. \begin{aligned} 2x - y &= 4 \\ x + 2y &= 7 \end{aligned} If (x, y) is the solution to the system of equations, what is the value of x + y?

Consider the system of equations below. \begin{aligned} 2x - y &= 4 \\ x + 2y &= 7 \end{al… — SAT

Consider the system of equations below.

\begin{aligned} 2x - y &= 4 \\ x + 2y &= 7 \end{aligned}

(x, y)

is the solution to the system of equations, what is the value of

x + y

The value of

x + y

is 5.

To solve the system, we can express

y

in terms of

x

from the first equation:

y = 2x - 4

. Substituting this into the second equation gives

x + 2(2x - 4) = 7

. Distributing the 2 gives

x + 4x - 8 = 7

, which simplifies to

5x - 8 = 7

. Adding 8 to both sides yields

5x = 15

, which gives

x = 3

. Substituting

x = 3

back into the first equation yields

2(3) - y = 4 \implies 6 - y = 4 \implies y = 2

. Thus, the value of

x + y

3 + 2 = 5

Express

y

in terms of

x

using the first equation.

y = 2x - 4

This sets up the system for solving by substitution.

Substitute the expression for

y

into the second equation and solve for

x

x + 2(2x - 4) = 7 \implies 5x - 8 = 7 \implies 5x = 15 \implies x = 3

This isolates and solves for the variable

x

Substitute the value of

x

back into the expression for

y

, then compute

x + y

y = 2(3) - 4 = 2

, and

x + y = 3 + 2 = 5

This finds the value of

y

and computes the final required sum.

Solving a system of linear equations in two variables to find the value of a linear combination.