If 3x + 5y = 11 and 4x + 9y = 3, what is the value of the expression x + 2y? — Armed Services Vocational Aptitude Battery (ASVAB)

If $3x + 5y = 11$ and $4x + 9y = 3$ , what is the value of the expression $x + 2y$ ?

A
22
B
4
2Answer
D
-2

Answer

The correct answer is 2. To solve the system, use the elimination method by multiplying the equations to create opposite or matching coefficients. Multiplying the first equation by 4 yields

12x + 20y = 44

. Multiplying the second equation by 3 yields

12x + 27y = 9

. Subtracting the first equation from the second gives

7y = -35

, so

y = -5

. Substituting

y = -5

into the first original equation gives

3x - 25 = 11

, which simplifies to

3x = 36

, or

x = 12

. Finally, substituting these values into the expression

x + 2y

gives

12 + 2(-5) = 12 - 10 = 2

Step-by-Step Solution

Multiply the first equation by 4 and the second equation by 3 to prepare for elimination.

12x + 20y = 44

and

12x + 27y = 9

Creating matching coefficients for

x

allows us to eliminate it by subtracting the equations.

Subtract the first new equation from the second new equation.

(12x + 27y) - (12x + 20y) = 9 - 44 \Rightarrow 7y = -35

This eliminates

x

and leaves a simple equation with only

y

Divide by 7 to solve for

y

y = -5

Isolating

y

gives its numerical value.

Substitute

y = -5

back into the original first equation (

3x + 5y = 11

) and solve for

x

3x + 5(-5) = 11 \Rightarrow 3x - 25 = 11 \Rightarrow 3x = 36 \Rightarrow x = 12

This finds the corresponding value for

x

Substitute

x = 12

and

y = -5

into the requested expression

x + 2y

12 + 2(-5) = 12 - 10 = 2

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

Key Concept

Solving systems of linear equations using the elimination method and evaluating algebraic expressions.

Estimated Time:2m 0s

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