SOLUTION: Linear System Extension Thinking & Inquiry Questions 8. A triangle is formed by the intersection of the lines 2x+3y=14, 4x-5y=-16, and the x-axis. Find the area of the triangle C

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Question 184612: Linear System Extension Thinking & Inquiry Questions
8. A triangle is formed by the intersection of the lines 2x+3y=14, 4x-5y=-16, and the x-axis. Find the area of the triangle
Could you help me please with this question because i am really confused. Thank you very much!!!
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Since the x axis forms one side of the triangle, use that as the base.

Find the x-intercepts of each of the two equations by substituting 0 for y in each of them. Then the length of the base of the triangle will be the magnitude of the difference between these x-intercepts.

Next find the point of intersection of the two lines represented by the two given equations by solving the 2-equation, 2-variable linear system. This one lends itself readily to solution by elimination if you go for eliminating the x term. Once you have that point of intersection, the y-coordinate will be the height of the triangle.

Now that you know the length of the base and the height, just use the triangle area formula:

John