Question 107814
1.

Solve by adding:

{{{-3x + 5y = 12}}}
{{{3x + 2y = 9}}}




If we add the two equations, we will get {{{0x + 7y = 21}}} or {{{7y = 21}}}. 

If we divide both sides by {{{7}}}, we get {{{y = 3}}}. 

Next, we substitute {{{3}}} in for {{{y}}} into any of given equations. 

If we choose to substitute in the first equation, we get{{{ -3x + 5(3) = 12}}}… ==> …{{{-3x + 15 = 12 }}}…==>… {{{ -3x = -3}}}…  ==>…  {{{x = 1}}}. 

So the two lines intersect at ({{{1}}}, {{{3}}}).



2.

Solve a system by substitution 

1st: Pick {{{1}}} equation and solve for {{{1}}} of the variables. 
  
{{{5x+4y=6}}}

{{{y =-2x+3 }}}

  
The second equation is already solved for {{{y}}}. 
  
"{{{-2x+3}}}" is the expression needed. 
  
2nd: Substitute this expression in the other equation. 

{{{5x+4y = 6}}}

{{{5x + 4(-2x + 3) = 6}}}

  
3rd: Sovle. 

{{{5x+4(-2x+3)= 6}}}

{{{5x-8x+12= 6}}}

{{{-3x+12= 6}}}

Add {{{-12}}} to the both sides

{{{-3x+12 – 12 = 6 - 12}}}

{{{-3x=  - 6}}}……..divide both sides by {{{-3}}}

{{{-3x/(-3) = -6/(-3)}}}

{{{x = 2}}}


  
4th: Use this new value in the step {{{1}}} equation to get the other variable. 

{{{y =-2x+3 }}}

{{{y =-2*2 + 3 }}}

{{{y = - 4 + 3 }}}

{{{y = - 1}}}


  
5th: State the solution and include values for both variables. 

{{{x = 2}}} 

{{{ y = -1 }}}


So the two lines intersect at ({{{2}}},{{{-1}}})