A system of linear equations is shown below. \begin{aligned} 5x - 2y &= 14 \\ 2x + y &= 11 \end{aligned} If (x, y) is the solution to the system of equations, what is the value of x?

A system of linear equations is shown below. \begin{aligned} 5x - 2y &= 14 \\ 2x + y &= 11… — SAT

A system of linear equations is shown below.

\begin{aligned} 5x - 2y &= 14 \\ 2x + y &= 11 \end{aligned}

(x, y)

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

x

The correct answer is

4

. Isolating

y

in the second equation gives

y = 11 - 2x

. Substituting this into the first equation yields

5x - 2(11 - 2x) = 14

. Distributing the

-2

results in

5x - 22 + 4x = 14

. Combining like terms simplifies the equation to

9x - 22 = 14

. Adding

22

to both sides gives

9x = 36

, and dividing by

9

yields

x = 4

Isolate

y

in the second equation.

y = 11 - 2x

This allows for substitution into the first equation.

Substitute the expression for

y

into the first equation.

5x - 2(11 - 2x) = 14

This creates an equation with only one variable,

x

Distribute the

-2

through the parentheses and combine like terms.

9x - 22 = 14

Distributing

-2

-2x

yields

+4x

, and combining

5x + 4x

gives

9x

Add

22

to both sides and divide by

9

x = 4

Isolating

x

gives the final value of the variable.

Solving systems of linear equations using the substitution method.