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

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3 Answers

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
 
 
 
 
-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  √
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