Question 133010
{{{x=y-4.2}}} Start with the first equation



{{{10x=10y-42}}} Multiply both sides by 10 to clear the decimal number



{{{10x-10y=-42}}} Subtract 10y from both sides





Start with the given system of equations:


{{{system(10x-10y=-42,2x-3y=-9)}}}




Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.





So let's isolate y in the first equation


{{{10x-10y=-42}}} Start with the first equation



{{{-10y=-42-10x}}}  Subtract {{{10x}}} from both sides



{{{-10y=-10x-42}}} Rearrange the equation



{{{y=(-10x-42)/(-10)}}} Divide both sides by {{{-10}}}



{{{y=((-10)/(-10))x+(-42)/(-10)}}} Break up the fraction



{{{y=x+21/5}}} Reduce




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


Since {{{y=x+21/5}}}, we can now replace each {{{y}}} in the second equation with {{{x+21/5}}} to solve for {{{x}}}




{{{2x-3highlight((x+21/5))=-9}}} Plug in {{{y=x+21/5}}} into the first equation. In other words, replace each {{{y}}} with {{{x+21/5}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{2x+(-3)(1)x+(-3)(21/5)=-9}}} Distribute {{{-3}}} to {{{x+21/5}}}



{{{2x-3x-63/5=-9}}} Multiply



{{{(5)(2x-3x-63/5)=(5)(-9)}}} Multiply both sides by the LCM of 5. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)




{{{10x-15x-63=-45}}} Distribute and multiply the LCM to each side




{{{-5x-63=-45}}} Combine like terms on the left side



{{{-5x=-45+63}}}Add 63 to both sides



{{{-5x=18}}} Combine like terms on the right side



{{{x=(18)/(-5)}}} Divide both sides by -5 to isolate x




{{{x=-18/5}}} Reduce






-----------------First Answer------------------------------



So the first part of our answer is: {{{x=-18/5}}}










Since we know that {{{x=-18/5}}} we can plug it into the equation {{{y=x+21/5}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=x+21/5}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=(-18/5)+21/5}}} Plug in {{{x=-18/5}}}



{{{y=-18/5+21/5}}} Multiply



{{{y=3/5}}} Combine like terms  (note: if you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>)




-----------------Second Answer------------------------------



So the second part of our answer is: {{{y=3/5}}}










-----------------Summary------------------------------


So our answers are:


{{{x=-18/5}}} and {{{y=3/5}}}


which form the point *[Tex \LARGE \left(-\frac{18}{5},\frac{3}{5}\right)]