Six times a number x, plus 4 times a number y, equals 14. Negative eight times x minus 4 times y equals -12. What are the number
s?
1 answer:
Converting this into an equation, we get:
6x+4y=14
-8x-4y=-12
We can solve this by adding the system of equations.
6x+4y=14
+ -8x-4y=-12
-------------------------
-2x=2
Simplifying, we get that x=-1. We can replug this into one of the equations to get y. We'll choose 6x+4y=14
Plugging in -1 for x, we get that:
6(-1)+4y=14
which is
-6+4y=14
which is
4y=20
Simplify this to get that y=5
To check, you can plug in x and y into both equations to make sure that they are true.
6(-1)+4(5)=14
-6+20=14
14=14 which is true
-8(-1)-4(5)=-12
8-20=-12
-12=-12 which is true
x=-1 and y=5
:)
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