-4x+7y=9 2y=-5x-22

Question

I need the ordered pair plz 

Answer 1

The easiest way to answer this problem algebraically is through elimination. Elimination is when you manipulate one or both of the equations through multiplying the whole equation so that when you add the two equations, one variable cancels.

 

In this case, it would help to get both problems arranged the same way. To do that, add 5x to both sides of the second equation, resulting in:

5x+2y=-22

 

Now line the two equations up on top of each other and choose which variable to eliminate.

 

-4x+7y=9

 5x+2y=-22

 

Let's eliminate the x. They already have opposite signs, so we just need to get the coefficients equal (except for the opposite signs--this will allow the x term to cancel through the properties of additive inverses). The least common multiple of 4 and 5 (the x coefficients) is 20, so we need to multiply the whole top equation by 5, and the whole bottom equation by 4.

 

5(-4x+7y)=5(9)

4( 5x+2y)=4(-22)

 

Resulting in the following equations to add together:

 

  -20x+35y=45

+ 20x+8y  =-88           Since -20x + 20x = 0x, the x term is eliminated.

--------------------

           43y =-43

               y =-1

 

If y=-1, then simply substitute -1 back in for y into one of the original equations to solve for x.

 

-4x+7(-1)=9

-4x - 7     =9

          -4x=16

             x=-4

 

Then put your ordered pair (-4, -1) into the second equation to check.

 

2(-1) = -5(-4)-22

-2     = 20-22

    -2 = -2

Check!

 

Answer 2

-4x+7y=9

2y=-5x-22

 

-4x=-7y+9

-5x=2y+22

-20x=-35y+45

20x=-8y-88

 

0=-43y-43

43y=-43

y=-1

 

-4x-7=9

-4x=16

x=-4

 

check:

-2=20-22

-2=-2