6x + 5y = 7 4x + 3y = 5 If (x, y) is the solution to the... | SAT Systems of two linear equations in two variables Question, Answer Explained

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Math · AlgebraMedium

$6x + 5y = 7$
$4x + 3y = 5$
If $(x, y)$ is the solution to the system of equations, what is the value of $x + y$ ?

$-1$

$1$

$2$

$12$

Show answer and explanation

Answer: B

Subtract the second equation from the first: $2x + 2y = 2$ . Divide both sides by $2$ : $x + y = 1$ . Solving fully gives $x = 2$ and $y = -1$ , which agrees.

Choice C is the value of $x$ alone. Adding $y = -1$ gives $x + y = 1$ .

Why the other choices are wrong

A. -1 is the value of y, not x + y.
C. 2 is the value of x. Add y = -1 to get x + y = 1.
D. Adding the equations gives 10x + 8y = 12, and 10x + 8y is not x + y.

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