SOLUTION: 4x+2y=-6 2x+3y=-3

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Question 221568: 4x+2y=-6
2x+3y=-3
Found 2 solutions by drj, jim_thompson5910:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
4x+2y=-6
2x+3y=-3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++4%5Cx+%2B+2%5Cy+=+-6%2C%0D%0A++++2%5Cx+%2B+3%5Cy+=+-3+%29%0D%0A++We'll use substitution. After moving 2*y to the right, we get:
4%2Ax+=+-6+-+2%2Ay, or x+=+-6%2F4+-+2%2Ay%2F4. Substitute that
into another equation:
2%2A%28-6%2F4+-+2%2Ay%2F4%29+%2B+3%5Cy+=+-3 and simplify: So, we know that y=0. Since x+=+-6%2F4+-+2%2Ay%2F4, x=-1.5.

Answer: system%28+x=-1.5%2C+y=0+%29.



I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%284x%2B2y=-6%2C2x%2B3y=-3%29


4x%2B2y=-6 Start with the first equation.


2y=-6-4x Subtract 4x from both sides.


y=%28-6-4x%29%2F%282%29 Divide both sides by 2 to isolate y.


y=-2x-3 Rearrange the terms and simplify.


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2x%2B3y=-3 Move onto the second equation.


2x%2B3%28-2x-3%29=-3 Now plug in y=-2x-3.


2x-6x-9=-3 Distribute.


-4x-9=-3 Combine like terms on the left side.


-4x=-3%2B9 Add 9 to both sides.


-4x=6 Combine like terms on the right side.


x=%286%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=-3%2F2 Reduce.


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


Since we know that x=-3%2F2, we can use this to find y.


4x%2B2y=-6 Go back to the first equation.


4%28-3%2F2%29%2B2y=-6 Plug in x=-3%2F2.


-6%2B2y=-6 Multiply.


2y=-6%2B6 Add 6 to both sides.


2y=0 Combine like terms on the right side.


y=%280%29%2F%282%29 Divide both sides by 2 to isolate y.


y=0 Reduce.


So the solutions are x=-3%2F2 and y=0.


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 4x%2B2y=-6 (red) and 2x%2B3y=-3 (green)