How do solve the following linear system?: -4x + 9y = 9 , -3x + 7y= -16 −4x+9y=9,−3x+7y=−16?
1 Answer
Explanation:
We will solve this using substitution (although you can solve it with other methods, I prefer this one).
First, we must rewrite the two equations and make sure they have an identical term. I will rewrite them as follows:
-4x + 9y = 9 −4x+9y=9 will become-12x + 27y = 27 −12x+27y=27
-3x + 7y = -16 −3x+7y=−16 will become-12x + 28y = -64 −12x+28y=−64
Now as you can see, both equations now have
We will rewrite one equation, let's use the first one, to isolate
-12x + 27y = 27 −12x+27y=27 will become-12x = 27 - 27y −12x=27−27y
Now we can substitute this into the second equation to find the first variable.
-12x + 28y = -64 −12x+28y=−64
(27 - 27y) + 28y = -64 (27−27y)+28y=−64
27 - 27y + 28y = -64 27−27y+28y=−64
27 + y = -64 27+y=−64
y = -91 y=−91
Now that we have found the value of
Take an original question, we'll use the first one, and substitute our
-4x + 9y = 9 −4x+9y=9
-4x + 9 (-91) = 9 −4x+9(−91)=9
-4x - 819 = 9 −4x−819=9
-4x = 828 −4x=828
x = -207 x=−207
So now we have solved the two equations to get