SOLUTION: hello im doing my homework and i dont get anything that i do can you please help me im on problem # 7 solve the system of equations x+4y=1 2x-3y=-9

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Question 187454This question is from textbook algebra 1 exloretions and applications
: hello
im doing my homework and i dont get anything that i do
can you please help me
im on problem # 7
solve the system of equations
x+4y=1
2x-3y=-9
 This question is from textbook algebra 1 exloretions and applications

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%28x%2B4y=1%2C2x-3y=-9%29


-2%28x%2B4y%29=-2%281%29 Multiply the both sides of the first equation by -2.


-2x-8y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-2x-8y=-2%2C2x-3y=-9%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:


%28-2x-8y%29%2B%282x-3y%29=%28-2%29%2B%28-9%29


%28-2x%2B2x%29%2B%28-8y%2B-3y%29=-2%2B-9 Group like terms.


0x%2B-11y=-11 Combine like terms.


-11y=-11 Simplify.


y=%28-11%29%2F%28-11%29 Divide both sides by -11 to isolate y.


y=1 Reduce.


------------------------------------------------------------------


-2x-8y=-2 Now go back to the first equation.


-2x-8%281%29=-2 Plug in y=1.


-2x-8=-2 Multiply.


-2x=-2%2B8 Add 8 to both sides.


-2x=6 Combine like terms on the right side.


x=%286%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=-3 Reduce.


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


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 x%2B4y=1 (red) and 2x-3y=-9 (green)