If 3x + y = 14 and x - 2y = -7, what is the value of x + y? — GRE General Test

If $3x + y = 14$ and $x - 2y = -7$ , what is the value of $x + y$ ?

Solving the linear system yields

x = 3

and

y = 5

. Adding these values together gives

3 + 5 = 8

, which is the correct answer.

Express

y

in terms of

x

using the first equation

y = 14 - 3x

Isolating one variable allows for direct substitution into the second equation.

Substitute

y = 14 - 3x

into the second equation

x - 2y = -7

x - 2(14 - 3x) = -7 \implies x - 28 + 6x = -7 \implies 7x = 21 \implies x = 3

Solving the single-variable equation gives the exact value for

x

Calculate

y

using

x = 3

y = 14 - 3(3) = 5

Substituting

x = 3

back into

y = 14 - 3x

gives the value for

y

Compute the sum

x + y

x + y = 3 + 5 = 8

The question specifically asks for the sum of both variables.

Solving a 2x2 System of Linear Equations by Substitution or Elimination

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