SOLUTION: Consider the following system of equations: {4x-7y=-5 5x+3y=29 Does the system have: one solution, no solution or infinite solutions?d

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Question 201817: Consider the following system of equations:
{4x-7y=-5
5x+3y=29
Does the system have: one solution, no solution or infinite solutions?d
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-7y=-5%2C5x%2B3y=29%29


3%284x-7y%29=3%28-5%29 Multiply the both sides of the first equation by 3.


12x-21y=-15 Distribute and multiply.


7%285x%2B3y%29=7%2829%29 Multiply the both sides of the second equation by 7.


35x%2B21y=203 Distribute and multiply.


So we have the new system of equations:
system%2812x-21y=-15%2C35x%2B21y=203%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:


%2812x-21y%29%2B%2835x%2B21y%29=%28-15%29%2B%28203%29


%2812x%2B35x%29%2B%28-21y%2B21y%29=-15%2B203 Group like terms.


47x%2B0y=188 Combine like terms.


47x=188 Simplify.


x=%28188%29%2F%2847%29 Divide both sides by 47 to isolate x.


x=4 Reduce.


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12x-21y=-15 Now go back to the first equation.


12%284%29-21y=-15 Plug in x=4.


48-21y=-15 Multiply.


-21y=-15-48 Subtract 48 from both sides.


-21y=-63 Combine like terms on the right side.


y=%28-63%29%2F%28-21%29 Divide both sides by -21 to isolate y.


y=3 Reduce.


So the solutions are x=4 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 4x-7y=-5 (red) and 5x%2B3y=29 (green)