how to solve -3x+7y=-16 and -9x+5y=16

Question

i dont know how to do this

please explain

Thanks

 

Answer 1

Hi Angelica;

-3x+7y=-16 and -9x+5y=16

The coefficients of x are -3 and -9.  These should be identical so we may apply the practice of elimination.

Let's take the first equation...

-3x+7y=-16

Let's multiply both sides by 3...

3(-3x+7y)=(-16)(3)

-9x+21y=-48

Let's subtract this from the second equation...

-9x+5y=16

-(-9x+21y=-48)

0-16y=64

The x is eliminated.

-16y=64

(-16y)/-16=64/-16

y=-4

Let's plug this into either equation to establish the value of x.  I randomly select the first...

-3x+7y=-16

-3x+[(7)(-4)]=-16

-3x-28=-16

Let's add 28 to both sides...

-3x-28+28=-16+28

-3x=12

Let's divide both sides by -3...

(-3x)/-3=12/-3

x=-4

Let's plug both values into the second equation to verify results...

-9x+5y=16

[(-9)(-4)]+[(5)(-4)]=16

A negative number multiplied by a negative number has a positive result...

36-20=16

16=16

 

 

 

 

Answer 2

-3x+7y=-16

-9x+5y=16

 

Let's multiply the first equation by -3 and add the resulting equation to the second equation:

 

 9x-21y=48
-9x+5y=16

 0 -16y=64

 

Divide both sides by -16:

 

y = -4

 

-9x+5(-4)=16

-9x = 16+20 = 36

x = -4

 

check:

 

-3(-4)+7(-4) =? -16

12-28 = -16  √

-9(-4)+5(-4) =? 16

36 - 20 = 16  √

Answer 3

Angelica ... you're just repeating the same problem ... follow the steps discussed in the original question on solving equations through elimination:  find a factor to multiply one or both equations so as to get a common term ... then, add or subtract one equation from the other.

 

multiplying the first by 3

-9x+21y=-48

-9x+5y=16

subtract one equation from the other

16y=-64

y=-4

-9x+5(-4)=16 ... -9x-20=16 ... -9x=36 ... x= 4