Question

Consider the following system of equations:

y = −2x + 3
y = x − 5

Which description best describes the solution to the system of equations?

Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.
Line y = −2x + 3 intersects line y = x − 5.
Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.
Line y = −2x + 3 intersects the origin.

Answer 1

Hi there!

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I believe your answer is:

"Line y = −2x + 3 intersects line y = x − 5."

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Here’s why:

• When the system of equations are graphed, they would intersect at a point.
• This means that there is a solution to the system. The solution is
  `((8)/(3) ,-(7)/(3) )`.
• While the statement that the lines intersect the x-axis is true, the question asks the statement that describes the solution.
• The solution is the point of intersection between the two lines.

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See the Graph Attached

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Hope this helps you. I apologize if it’s incorrect.