Question 141086
Do you want to use substitution to solve this?



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.



{{{y+7x=46}}} Start with the second equation (Either equation will work, but y is easier to isolate in this equation)



{{{y=46-7x}}}  Subtract {{{7x}}} from both sides



{{{y=-7x+46}}} Rearrange the equation


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


Since {{{y=-7x+46}}}, we can now replace each {{{y}}} in the first equation with {{{-7x+46}}} to solve for {{{x}}}




{{{2x+3highlight((-7x+46))=24}}} Plug in {{{y=-7x+46}}} into the first equation. In other words, replace each {{{y}}} with {{{-7x+46}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{2x+(3)(-7)x+(3)(46)=24}}} Distribute {{{3}}} to {{{-7x+46}}}



{{{2x-21x+138=24}}} Multiply



{{{-19x+138=24}}} Combine like terms on the left side



{{{-19x=24-138}}}Subtract 138 from both sides



{{{-19x=-114}}} Combine like terms on the right side



{{{x=(-114)/(-19)}}} Divide both sides by -19 to isolate x




{{{x=6}}} Divide






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



So the first part of our answer is: {{{x=6}}}










Since we know that {{{x=6}}} we can plug it into the equation {{{y=-7x+46}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-7x+46}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-7(6)+46}}} Plug in {{{x=6}}}



{{{y=-42+46}}} Multiply



{{{y=4}}} Combine like terms 




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



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










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


So our answers are:


{{{x=6}}} and {{{y=4}}}


which form the point *[Tex \LARGE \left(6,4\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(6,4\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  graph(500, 500, -10,10,-10,10, (46-7*x)/(1), (24-2*x)/(3) ),
  blue(circle(6,4,0.1)),
  blue(circle(6,4,0.12)),
  blue(circle(6,4,0.15))
)
}}} graph of {{{7x+y=46}}} (red) and {{{2x+3y=24}}} (green)  and the intersection of the lines (blue circle).