Question 145330
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<a href="#two">Jump to problem # 2</a>

# 1


Start with the given system of equations:


{{{system(x+y=15,4x+3y=38)}}}




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


{{{x+y=15}}} Start with the first equation



{{{y=15-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+15}}} Rearrange the equation




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


Since {{{y=-x+15}}}, we can now replace each {{{y}}} in the second equation with {{{-x+15}}} to solve for {{{x}}}




{{{4x+3highlight((-x+15))=38}}} Plug in {{{y=-x+15}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+15}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{4x+(3)(-1)x+(3)(15)=38}}} Distribute {{{3}}} to {{{-x+15}}}



{{{4x-3x+45=38}}} Multiply



{{{x+45=38}}} Combine like terms on the left side



{{{x=38-45}}}Subtract 45 from both sides



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






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



So the first part of our answer is: {{{x=-7}}}










Since we know that {{{x=-7}}} we can plug it into the equation {{{y=-x+15}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+15}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(-7)+15}}} Plug in {{{x=-7}}}



{{{y=7+15}}} Multiply



{{{y=22}}} Combine like terms 




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



So the second part of our answer is: {{{y=22}}}










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


So our answers are:


{{{x=-7}}} and {{{y=22}}}


which form the point *[Tex \LARGE \left(-7,22\right)] 




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<a name="two">


<a href="#one">Jump to problem # 1</a>

# 2


Start with the given system of equations:


{{{system(-3x+y=-4,x-y=0)}}}




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


{{{-3x+y=-4}}} Start with the first equation



{{{y=-4+3x}}} Add {{{3x}}} to both sides



{{{y=+3x-4}}} Rearrange the equation



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


Since {{{y=3x-4}}}, we can now replace each {{{y}}} in the second equation with {{{3x-4}}} to solve for {{{x}}}




{{{x-highlight((3x-4))=0}}} Plug in {{{y=3x-4}}} into the first equation. In other words, replace each {{{y}}} with {{{3x-4}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x-3x+4=0}}} Distribute the negative



{{{-2x+4=0}}} Combine like terms on the left side



{{{-2x=0-4}}}Subtract 4 from both sides



{{{-2x=-4}}} Combine like terms on the right side



{{{x=(-4)/(-2)}}} Divide both sides by -2 to isolate x




{{{x=2}}} Divide






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



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










Since we know that {{{x=2}}} we can plug it into the equation {{{y=3x-4}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=3x-4}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=3(2)-4}}} Plug in {{{x=2}}}



{{{y=6-4}}} Multiply



{{{y=2}}} Combine like terms 




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



So the second part of our answer is: {{{y=2}}}










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


So our answers are:


{{{x=2}}} and {{{y=2}}}


which form the point *[Tex \LARGE \left(2,2\right)]