SOLUTION: please help me with {2x+3y=0 x+2y=-1 where do i start

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Question 952150: please help me with {2x+3y=0 x+2y=-1 where do i start
Found 2 solutions by MathLover1, macston:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B3y=0.......eq.1
x%2B2y=-1.......eq.2
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you are given a system of two linear equations and you need to find x and y that make true both equations, and that will be coordinates of the point where these two lines intersect

2x%2B3y=0.......eq.1
x%2B2y=-1.......eq.2....both side multiply by 2
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2x%2B3y=0.......eq.1
2x%2B4y=-2.......eq.2
----------------------- ------subtract eq.2 from eq.1
2x%2B3y-%282x%2B4y%29=0-%28-2%29
2x%2B3y-2x-4y=2
cross%282x%29%2B3y-cross%282x%29-4y=2
3y-4y=2
-y=2
y=-2
highlight%28y=-2%29
substitute -2 for y in one of the given equations and solve for x
x%2B2y=-1.......eq.2
x%2B2%2A%28-2%29=-1
x-4=-1
x=4-1
highlight%28x=3%29
so, solution to your system is:(highlight%283%29,highlight%28-2%29)





Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3y=0
x+2y=-1 Solve for x.
x=-1-2y Substitute in first equation for x.
2(-1-2y)+3y=0
-2-4y+3y=0 Add 2 to each side
-y=2 Multiply each side by -1.
y=-2 ANSWER 1: y=-2 Use this value of y to back solve one of the original equations.
2x+3y=0
2x+3(-2)=0
2x-6=0 Add 6 to each side.
2x=6 Divide each side by 2.
x=3 ANSWER 2: x=3 The solution to the system of equations is (3,-2).
CHECK:
Use equation not used for back solving:
x+2y=-1
3+2(-2)=-1
3-4=-1
-1=-1