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QuizMultiple Choice

Solving Systems of Linear Equations: Linear Combinations

Question 1 • TX-Algebra I A-CR

Which statement describes the graph of the system of equations below?1.5x + 0.2y = 2.681.6x + 0.3y = 2.98

Answer
A
The lines are parallel.
B
The lines overlap at all points.
C
The lines intersect at (1.6,1.4).
D
The lines intersect at (3.1,0.5).

Explanation

Substitute (1.6, 1.4) into both equations. In the first, 1.5(1.6) + 0.2(1.4) = 2.4 + 0.28 = 2.68; in the second, 1.6(1.6) + 0.3(1.4) = 2.56 + 0.42 = 2.98. Since the point satisfies both equations, the lines intersect at (1.6, 1.4), so the correct choice is “The lines intersect at (1.6, 1.4).”

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