Question 125748
Do you want to solve this system by substitution?





Start with the given system of equations:


{{{system(7x+2y=9,3x+8y=11)}}}




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


{{{7x+2y=9}}} Start with the first equation



{{{2y=9-7x}}}  Subtract {{{7x}}} from both sides



{{{2y=-7x+9}}} Rearrange the equation



{{{y=(-7x+9)/(2)}}} Divide both sides by {{{2}}}



{{{y=((-7)/(2))x+(9)/(2)}}} Break up the fraction



{{{y=(-7/2)x+9/2}}} Reduce




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


Since {{{y=(-7/2)x+9/2}}}, we can now replace each {{{y}}} in the second equation with {{{(-7/2)x+9/2}}} to solve for {{{x}}}




{{{3x+8highlight(((-7/2)x+9/2))=11}}} Plug in {{{y=(-7/2)x+9/2}}} into the first equation. In other words, replace each {{{y}}} with {{{(-7/2)x+9/2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{3x+(8)(-7/2)x+(8)(9/2)=11}}} Distribute {{{8}}} to {{{(-7/2)x+9/2}}}



{{{3x-(56/2)x+72/2=11}}} Multiply



{{{(2)(3x-(56/2)x+72/2)=(2)(11)}}} 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>)




{{{6x-56x+72=22}}} Distribute and multiply the LCM to each side




{{{-50x+72=22}}} Combine like terms on the left side



{{{-50x=22-72}}}Subtract 72 from both sides



{{{-50x=-50}}} Combine like terms on the right side



{{{x=(-50)/(-50)}}} Divide both sides by -50 to isolate x




{{{x=1}}} Divide






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



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










Since we know that {{{x=1}}} we can plug it into the equation {{{y=(-7/2)x+9/2}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=(-7/2)x+9/2}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=(-7/2)(1)+9/2}}} Plug in {{{x=1}}}



{{{y=-7/2+9/2}}} Multiply



{{{y=1}}} Combine like terms and reduce.  (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=1}}}










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


So our answers are:


{{{x=1}}} and {{{y=1}}}


which form the point *[Tex \LARGE \left(1,1\right)] 









Now let's graph the two equations (if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)



From the graph, we can see that the two equations intersect at *[Tex \LARGE \left(1,1\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  graph(500, 500, -10,10,-10,10, (9-7*x)/(2), (11-3*x)/(8) ),
  blue(circle(1,1,0.1)),
  blue(circle(1,1,0.12)),
  blue(circle(1,1,0.15))
)
}}} graph of {{{7x+2y=9}}} (red) and {{{3x+8y=11}}} (green)  and the intersection of the lines (blue circle).