SOLUTION: i've tried several different ways and can not seem to get this question of elimination, 5y-7x=29 2y+x=4 the x should equal -2 and y should equal 3 i know this because i use

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: i've tried several different ways and can not seem to get this question of elimination, 5y-7x=29 2y+x=4 the x should equal -2 and y should equal 3 i know this because i use      Log On


   

Question 176030: i've tried several different ways and can not seem to get this question of elimination,
5y-7x=29
2y+x=4
the x should equal -2 and y should equal 3
i know this because i used substitution earlier for this question,
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I've rearranged the terms to get the system

system%28-7x%2B5y=29%2Cx%2B2y=4%29




Start with the given system of equations:
system%28-7x%2B5y=29%2Cx%2B2y=4%29


7%28x%2B2y%29=7%284%29 Multiply the both sides of the second equation by 7.


7x%2B14y=28 Distribute and multiply.


So we have the new system of equations:
system%28-7x%2B5y=29%2C7x%2B14y=28%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:


%28-7x%2B5y%29%2B%287x%2B14y%29=%2829%29%2B%2828%29


%28-7x%2B7x%29%2B%285y%2B14y%29=29%2B28 Group like terms.


0x%2B19y=57 Combine like terms.


19y=57 Simplify.


y=%2857%29%2F%2819%29 Divide both sides by 19 to isolate y.


y=3 Reduce.


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


-7x%2B5y=29 Now go back to the first equation.


-7x%2B5%283%29=29 Plug in y=3.


-7x%2B15=29 Multiply.


-7x=29-15 Subtract 15 from both sides.


-7x=14 Combine like terms on the right side.


x=%2814%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=-2 Reduce.


So our answer is x=-2 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 -7x%2B5y=29 (red) and x%2B2y=4 (green)