A set of equations is given below: Equation C: y = 4x + 8 Equation D: y = 4x + 2 Which of the following best describes the solution to the given set of equations?

Question

A set of equations is given below:

Equation C: y = 4x + 8

Equation D: y = 4x + 2

Which of the following best describes the solution to the given set of equations?

 No solution One solution Two solutions Infinitely many solutions

Answer 1

The lines have the same slope but different y intercepts. The lines are parallel and never meet.

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Answer 2

Hi Norma,

This question may be answered one of two ways: algebraically or graphically.

Algebraically

Solve the set of equations by equating both equations and solving for x.

4x + 8 = 4x + 2

8 = 2

8 is never equal to 2 so the set of equations has no solution.

Graphically

Equation C describes a line with a slope of 4 and a y-intercept of 8.

Equation D describes a line with a slope of 4 and a y-intercept of 2.

Because the two lines have the same slope but different y-intercepts, they are parallel.

Parallel lines never intersect so the set of equations has no solution.