SOLUTION: Solve the following system of equations algebraically and check: 4x - 5y = 18 3x - 2y = 10

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Question 252498: Solve the following system of equations algebraically and check:
4x - 5y = 18
3x - 2y = 10
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-5y=18%2C3x-2y=10%29


2%284x-5y%29=2%2818%29 Multiply the both sides of the first equation by 2.


8x-10y=36 Distribute and multiply.


-5%283x-2y%29=-5%2810%29 Multiply the both sides of the second equation by -5.


-15x%2B10y=-50 Distribute and multiply.


So we have the new system of equations:
system%288x-10y=36%2C-15x%2B10y=-50%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%288x-10y%29%2B%28-15x%2B10y%29=%2836%29%2B%28-50%29


%288x%2B-15x%29%2B%28-10y%2B10y%29=36%2B-50 Group like terms.


-7x%2B0y=-14 Combine like terms.


-7x=-14 Simplify.


x=%28-14%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=2 Reduce.


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8x-10y=36 Now go back to the first equation.


8%282%29-10y=36 Plug in x=2.


16-10y=36 Multiply.


-10y=36-16 Subtract 16 from both sides.


-10y=20 Combine like terms on the right side.


y=%2820%29%2F%28-10%29 Divide both sides by -10 to isolate y.


y=-2 Reduce.


So the solutions are x=2 and y=-2.


Which form the ordered pair .


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-5y=18 (red) and 3x-2y=10 (green)