SOLUTION: Solve the following system of equations. What is the value of x? 2x + 3y = 7 5x + 4y = 7

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Question 207021: Solve the following system of equations. What is the value of x?
2x + 3y = 7
5x + 4y = 7
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%2B3y=7%2C5x%2B4y=7%29


5%282x%2B3y%29=5%287%29 Multiply the both sides of the first equation by 5.


10x%2B15y=35 Distribute and multiply.


-2%285x%2B4y%29=-2%287%29 Multiply the both sides of the second equation by -2.


-10x-8y=-14 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B15y=35%2C-10x-8y=-14%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:


%2810x%2B15y%29%2B%28-10x-8y%29=%2835%29%2B%28-14%29


%2810x%2B-10x%29%2B%2815y%2B-8y%29=35%2B-14 Group like terms.


0x%2B7y=21 Combine like terms.


7y=21 Simplify.


y=%2821%29%2F%287%29 Divide both sides by 7 to isolate y.


y=3 Reduce.


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10x%2B15y=35 Now go back to the first equation.


10x%2B15%283%29=35 Plug in y=3.


10x%2B45=35 Multiply.


10x=35-45 Subtract 45 from both sides.


10x=-10 Combine like terms on the right side.


x=%28-10%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=-1 Reduce.


So the solutions are x=-1 and y=3.


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 2x%2B3y=7 (red) and 5x%2B4y=7 (green)