SAT Mathematics Practice Test 6

Adding the equations side-by-side eliminates y, as shown below.
$7\mathit{x}+3\mathit{y}=8$
$6\mathit{x}-3\mathit{y}=5$
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$13\mathit{x}+0=13$
Solving the obtained equation for x gives $\mathit{x}=1$. Substituting 1 for x in the first equation gives $7\left(1\right)+3\mathit{y}=8$ Subtracting 7 from both sides of the equation yields $$3\mathit{y}=1$$, so $\mathit{y}=\frac{1}{3}$ Therefore, the value of $\mathit{x}-\mathit{y}$ is $1-\frac{1}{3},$ or $\frac{2}{3}$
Choice C is incorrect because $1+\frac{1}{3}=\frac{4}{3}$ is the value of $\mathit{x}+\mathit{y}$, not $\mathit{x}-\mathit{y}$. Choices A and D areincorrect and may be the result of some computational errors.