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Systems of two linear equations in two variables SAT question

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

A system of two linear equations is graphed in the xy-plane below.

The figure presents the graph of 2 lines in the x y plane. The numbers negative 4 through 16, in increments of 2, are indicated on the x axis. The numbers negative 4 through 20, in increments of 2, are indicated on the y axis. One line begins above the x axis and to the left of the y axis. It moves upward and to the right, crossing the y axis at 6, and passing through the point with coordinates 3 comma 9 and the point with coordinates 12 comma 18. The other line begins below the x axis and to the left of the y axis. It moves upward and to the right, crossing the y axis at 3, and passing through the point with coordinates 3 comma 9 and the point with coordinates 6 comma 15. The two lines intersect at the point with coordinates 3 comma 9.

Which of the following points is the solution to the system of equations?

ExplanationShow

Choice A is correct. The solution to this system of linear equations is the point that lies on both lines graphed, or the point of intersection of the two lines. According to the graphs, the point of intersection occurs when $x equals 3$ and $y equals 9$ , or at the point $with coordinates 3 comma 9$ .

Choices B and D are incorrect. Each of these points lies on one line, but not on both lines in the xy-plane. Choice C is incorrect. This point doesn’t lie on either of the lines graphed in the xy-plane.

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Systems of two linear equations in two variables SAT question

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