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Systems of two linear equations in two variables SAT question

Math · Algebra · Medium · Answer it here, explanation included.

Equation 1: 5 x plus 3 y, equals 38; Equation 2: x plus 3 y, equals 10

In the solution x comma y to the system of equations above, what is the value of x ?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

The correct answer is 7. Subtracting the second equation from the first equation eliminates the variable y.

Equation 1, 5 x, plus 3 y, equals 38; Equation 2,  x plus 3 y, equals 10; Subtracting equation 2 from equation 1 yields equation 3, which is 4 x, equals 28.

Dividing both sides of the resulting equation by 4 yields x = 7.

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