Question

Solving systems of linear equations by graphing 2x+3y=-12 and 10x+3y=12

Answer 1

Answer:

  (x, y) = (3, -6)

Step-by-step explanation:

I like a good graphing calculator for solving systems of equations by graphing.

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If you're solving these by hand, you need to graph the equations. It can be convenient to put the equations into "intercept form" so you can use the x- and y-intercepts to draw your graph.

That form is ...

  x/(x-intercept) +y/(y-intercept) = 1

Dividing a standard-form equation by the constant on the right will put it in this form.

  x/(-12/2) +y/(-12/3) = 1 . . . . . . divide the first equation by -12

  x/(-6) +y/(-4) = 1 . . . . . . . . . . . the x-intercept is -6; the y-intercept is -4

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  x/(12/10) +y/(12/3) = 1 . . . . . . divide the second equation by 12

  x/1.2 +y/4 = 1 . . . . . . . . . . . . . the x-intercept is 1.2*; the y-intercept is 4

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The locations of these intercepts and the slopes of the lines tell you that the solution will be in the fourth quadrant. The lines intersect at (x, y) = (3, -6).

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* It can be difficult to draw an accurate graph using an intercept point that is not on a grid line. It may be desirable to put the second equation into slope-intercept form, so you can see the rise/run values that let you choose grid points on the line. That equation is y =-10/3x +4. A "rise" of -10 for a "run" of +3 will get you to (3, -6) starting from the y-intercept of (0, 4).