Question 196595
{{{x + y = 7/2}}} Start with the first equation.



{{{2x+2y=7}}} Multiply every term by 2 to clear out the fraction.




So we have the system of equations:


{{{system(2x+2y=7,4x-3y=-14)}}}




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


{{{2x+2y=7}}} Start with the first equation



{{{2y=7-2x}}}  Subtract {{{2x}}} from both sides



{{{2y=-2x+7}}} Rearrange the equation



{{{y=(-2x+7)/(2)}}} Divide both sides by {{{2}}}



{{{y=((-2)/(2))x+(7)/(2)}}} Break up the fraction



{{{y=-x+7/2}}} Reduce




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


Since {{{y=-x+7/2}}}, we can now replace each {{{y}}} in the second equation with {{{-x+7/2}}} to solve for {{{x}}}




{{{4x-3highlight((-x+7/2))=-14}}} Plug in {{{y=-x+7/2}}} into the second equation. In other words, replace each {{{y}}} with {{{-x+7/2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{4x+(-3)(-1)x+(-3)(7/2)=-14}}} Distribute {{{-3}}} to {{{-x+7/2}}}



{{{4x+3x-21/2=-14}}} Multiply



{{{(2)(4x+3x-21/2)=(2)(-14)}}} Multiply both sides by the LCM of 2. 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>)




{{{8x+6x-21=-28}}} Distribute and multiply the LCM to each side




{{{14x-21=-28}}} Combine like terms on the left side



{{{14x=-28+21}}}Add 21 to both sides



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



{{{x=(-7)/(14)}}} Divide both sides by 14 to isolate x




{{{x=-1/2}}} Reduce






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



So the first part of our answer is: {{{x=-1/2}}}










Since we know that {{{x=-1/2}}} we can plug it into the equation {{{y=-x+7/2}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+7/2}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(-1/2)+7/2}}} Plug in {{{x=-1/2}}}



{{{y=1/2+7/2}}} Multiply



{{{y=4}}} Combine like terms and reduce. 



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



So the second part of our answer is: {{{y=4}}}










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


So our answers are:


{{{x=-1/2}}} and {{{y=4}}}


which form the ordered pair *[Tex \LARGE \left(-\frac{1}{2},4\right)]