If 3x + 2y = 18 and x + 4y = 16, what is the value of x + y? — GMAT

If $3x + 2y = 18$ and $x + 4y = 16$ , what is the value of $x + y$ ?

Solving the system of linear equations

3x + 2y = 18

and

x + 4y = 16

yields

x = 4

and

y = 3

. Adding these values together produces

4 + 3 = 7

Express

x

in terms of

y

using the second equation

x = 16 - 4y

Isolating one variable allows straightforward substitution into the other equation.

Substitute

x = 16 - 4y

into the first equation

3(16 - 4y) + 2y = 18 \implies 48 - 12y + 2y = 18 \implies 48 - 10y = 18

This creates an equation containing only the variable

y

Solve for

y

-10y = 18 - 48 = -30 \implies y = 3

Isolating the numerical term isolates the value of

y

Substitute

y = 3

back to find

x

x = 16 - 4(3) = 16 - 12 = 4

Determines the specific value of

x

Calculate the requested sum

x + y

x + y = 4 + 3 = 7

Provides the final requested expression value.

Solving a system of linear equations by substitution or elimination to evaluate a combined linear expression.

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