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1.4 Systems of Two Linear Equations - Graphical solution of two lines
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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 indied 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?

A.

Equation 1: y equals 0. Equation 2: x equals 1

B.

Equation 1: y equals 1. Equation 2: x equals 0

C.

Equation 1: y equals 0. Equation 2: x equals three halves

D.

Equation 1: y equals three halves. Equation 2: x equals 0

Which of the following systems of equations has the same solution as the system of equations

Hard-difficulty · SAT Math · Systems of Two Linear Equations — Graphical solution of two lines. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.

 

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