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Algebra / Systems of two linear equations in two variables Difficulty: Medium

The figure presents the graph of two intersecting lines in the x y plane with the origin labeled O. The integers negative 5 through 5 are indicated on each axis. One line begins above the x axis and to the left of the y axis, and trends downward and to the right. It crosses the y axis between 0 and 1, then crosses the x axis between 1 and 2, and ends below the x axis and to the right of the y axis. The other line begins below the x axis and slightly to the left of the y axis, and trends upward and to the right. It crosses the y axis at negative 5, then crosses the x axis between 1 and 2, and ends above the x axis and to the right of the y axis. The two lines intersect at the point where both lines cross the x axis between 1 and 2.

Which of the following systems of equations has the same solution as the system of equations graphed above?

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Explanation

Choice A is correct. The solution to a system of equations is the coordinates of the intersection point of the graphs of the equations in the xy-plane. Based on the graph, the solution to the given system of equations is best approximated as $the point with coordinates three halves comma 0$ . In the xy-plane, the graph of $y equals 0$ is a horizontal line on which every y-coordinate is 0, and the graph of $x equals three halves$ is a vertical line on which every x-coordinate is $three halves$ . These graphs intersect at the point $with coordinates three halves comma 0$ . Therefore, the system of equations in choice A has the same solution as the given system.

Choices B, C, and D are incorrect. If graphed in the xy-plane, these choices would intersect at the points $with coordinates 0 comma three halves$ , $1 comma 0$ , and $0 comma 1$ , respectively, not $the point with coordinates three halves comma 0$ .