##### How do I solve a system of linear equations by graphing?

 Algebra Tutor: None Selected Time limit: 1 Day

Nov 13th, 2014

• Solve the following system by graphing.
• 2x – 3y = –2
4
x +  y = 24

I know I need a neat graph, so I'll grab my ruler and get started. First, I'll solve each equation for "y=", so I can graph easily:

2x – 3y = –2
2x + 2 = 3y(2/3)x + (2/3) = y

4x + y = 24
y = –4x + 24

The second line will be easy to graph using just the slope and intercept, but I'll need a T-chart for the first line.

 x y = (2/3)x + (2/3) y = –4x + 24 –4 –8/3 + 2/3 = –6/3 = –2 16 + 24 = 40 –1 –2/3 + 2/3 = 0 4 + 24 = 28 2 4/3 + 2/3 = 6/3 = 2 –8 + 24 = 16 5 10/3 + 2/3 = 12/3 = 4 –20 + 24 = 4 8 16/3 + 2/3 = 18/3 = 6 –32 + 24 = –8

(Sometimes you'll notice the intersection right on the T-chart. Do you see the point that is in both equations above? Check the gray-shaded row above.)

 Now that I have some points, I'll grab my ruler and graph neatly, and look for the intersection: Even if I hadn't noticed the intersection point in the T-chart, I can certainly see it from the picture.

solution:  (x, y) = (5, 4)

Nov 13th, 2014

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Nov 13th, 2014
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Nov 13th, 2014
Dec 9th, 2016
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