If (x, y) is the solution to the system of equations below, what is the value of the expre… — Armed Services Vocational Aptitude Battery (ASVAB)

If $(x, y)$ is the solution to the system of equations below, what is the value of the expression $x + 3y$ ?

3x - 2y = 14

x = y + 5

The value of the expression is 1.

The system can be efficiently solved using substitution because the second equation already isolates

x

. Substituting

x = y + 5

into the first equation yields

3(y + 5) - 2y = 14

. Distributing the

3

gives

3y + 15 - 2y = 14

, which simplifies to

y = -1

. Substituting this back into the second equation gives

x = -1 + 5 = 4

. Finally, the question asks for the value of

x + 3y

, which evaluates to

4 + 3(-1) = 1

Substitute the expression for

x

from the second equation into the first equation.

3(y + 5) - 2y = 14

This isolates a single variable, allowing us to solve for

y

Distribute the 3 and solve the resulting equation for

y

3y + 15 - 2y = 14 \Rightarrow y + 15 = 14 \Rightarrow y = -1

Expanding the terms allows combining like terms to find the value of

y

Substitute

y = -1

back into the second equation to determine

x

x = -1 + 5 \Rightarrow x = 4

Both values are needed for the final expression.

Evaluate the target expression

x + 3y

using the values found for

x

and

y

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

The question specifically asks for the evaluated value of this expression, not just the ordered pair.

Solving a system of linear equations using the substitution method and evaluating an algebraic expression.

Question