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Identify the coordinates (x,y) of the solution for the following system of equations by graphing.  Type your answer below in the form (x,y)5x + 6y = 54−x + y = 9

Question

Identify the coordinates (x,y) of the solution for the following system of equations by graphing.  Type your answer below in the form (x,y)5x + 6y = 54−x + y = 9

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Solution

To solve the system of equations by graphing, follow these steps:

  1. Rewrite each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

The first equation is 5x + 6y = 54. To isolate y, subtract 5x from both sides and then divide by 6 to get y = -(5/6)x + 9.

The second equation is -x + y = 9. To isolate y, add x to both sides to get y = x + 9.

  1. Graph both equations on the same set of axes.

The first line has a slope of -5/6 and a y-intercept of 9. The second line has a slope of 1 and a y-intercept of 9.

  1. Identify the point where the two lines intersect. This point is the solution to the system of equations.

By graphing these two lines, you will find that they intersect at the point (0,9).

So, the solution to the system of equations is (0,9).

This problem has been solved

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