If real numbers x and y satisfy the system of linear equations: 7x + 4y = 113 3x + 6y = 87… — GMAT

If real numbers $x$ and $y$ satisfy the system of linear equations:

7x + 4y = 113

3x + 6y = 87

what is the value of $x + y$ ?

Answer: 20

The value of

x + y

is 20.

Adding the two equations yields

10x + 10y = 200

. Dividing the entire equation by 10 directly gives

x + y = 20

. Alternatively, solving the system yields

x = 11

and

y = 9

, whose sum is

11 + 9 = 20

Add the two equations together to combine like terms.

(7x + 4y) + (3x + 6y) = 113 + 87 \implies 10x + 10y = 200

Recognizing that adding the equations creates symmetric coefficients of 10 for both

x

and

y

allows a direct solution for the sum

(x + y)

Divide the combined equation by 10.

\frac{10(x + y)}{10} = \frac{200}{10} \implies x + y = 20

Isolating

(x + y)

directly avoids the extra computation of solving for

x

and

y

individually.

Solving Systems of Linear Equations by Combination

Estimated Time:1m 30s

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