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What is the solution to this system of equations?

4x−3y=26
3x+2y=11

5,2
8,2
-2,5
5,-2

User Janaz
by
8.0k points

1 Answer

1 vote

Answer:

(x, y) = (5, -2)

Explanation:

A graphing calculator provides a quick and easy way to find the solution.

_____

There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:

The intercepts of the first equation are ...

  • x-intercept = 26/4 = 6 1/2
  • y-intercept = -26/3 = -8 2/3

So the graph of it will form a triangle with the axes in the 4th quadrant.

The intercepts of the second equation are ...

  • x-intercept = 11/3 = 3 2/3
  • y-intercept = 11/2 = 5 1/2

So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.

The only 4th-quadrant answer choice is (5, -2).

What is the solution to this system of equations? 4x−3y=26 3x+2y=11 5,2 8,2 -2,5 5,-2-example-1
User Latorrefabian
by
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