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

$Equation 1: x plus 5 y, equals 5. Equation 2: 2 x minus y, equals negative 4$

Which of the following graphs in the xy-plane could be used to solve the system of equations above?

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Explanation

Choice C is correct. The graph of a system of equations is the graph that shows the lines represented by each of the equations in the system. The x-intercept of the graph of each given equation can be found by substituting 0 for y in each equation: $x plus, 5 times 0, equals 5$ , or $x equals 5$ , and $2 x minus 0, equals negative 4$ , or $x equals negative 2$ . The y-intercept of the graph of each equation can be found by substituting 0 for x in each equation: $0 plus 5 y, equals 5$ , or $y equals 1$ , and $2 times 0, minus y, equals negative 4$ or $y equals 4$ . Using these x- and y- intercept values, the line that has equation $x plus 5 y, equals 5$ passes through the points $with coordinates 0 comma 1$ and $5 comma 0$ , and the line that has equation $2 x minus y, equals negative 4$ passes through the points $with coordinates 0 comma 4$ and $negative 2 comma 0$ . Only the lines in choice C pass through these points and can be used to solve the given system of equations.

Choices A, B, and D are incorrect. In choices A and B, neither line passes through $the points with coordinates 0 comma 1$ and $5 comma 0$ or $the points with coordinates 0 comma 4$ and $negative 2 comma 0$ . In choice D, although one line passes through $the points with coordinates 0 comma 4$ and $negative 2 comma 0$ the other line doesn’t pass through $the points with coordinates 0 comma 1$ and $5 comma 0$ .