SOLUTION: Explain how to apply elimination in solving a system of equations; apply substitution in solving a system of equations. Demonstrate each technique in solving the system 2x + 7y

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Question 202943: Explain how to apply elimination in solving a system of equations; apply substitution in solving a system of equations. Demonstrate each technique in solving the system
2x + 7y = 12
5x - 4y = -13
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%282x%2B7y=12%2C5x-4y=-13%29


2x%2B7y=12 Start with the first equation.


7y=12-2x Subtract 2x from both sides.


y=%2812-2x%29%2F%287%29 Divide both sides by 7 to isolate y.


y=-%282%2F7%29x%2B12%2F7 Rearrange the terms and simplify.


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5x-4y=-13 Move onto the second equation.


5x-4%28-%282%2F7%29x%2B12%2F7%29=-13 Now plug in y=-%282%2F7%29x%2B12%2F7.


5x%2B%288%2F7%29x-48%2F7=-13 Distribute.


7%285x%2B%288%2Fcross%287%29%29x-48%2Fcross%287%29%29=7%28-13%29 Multiply both sides by the LCD 7 to clear any fractions.


35x%2B8x-48=-91 Distribute and multiply.


43x-48=-91 Combine like terms on the left side.


43x=-91%2B48 Add 48 to both sides.


43x=-43 Combine like terms on the right side.


x=%28-43%29%2F%2843%29 Divide both sides by 43 to isolate x.


x=-1 Reduce.


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Since we know that x=-1, we can use this to find y.


2x%2B7y=12 Go back to the first equation.


2%28-1%29%2B7y=12 Plug in x=-1.


-2%2B7y=12 Multiply.


7y=12%2B2 Add 2 to both sides.


7y=14 Combine like terms on the right side.


y=%2814%29%2F%287%29 Divide both sides by 7 to isolate y.


y=2 Reduce.


So the solutions are x=-1 and y=2.


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 2x%2B7y=12 (red) and 5x-4y=-13 (green)