Question 5043
Y=3x - 2
Y=-1/2x + 5


Substitution method means to substitute x or y from one equation into the other equation.  In this case, since both equations are in "Y= " format, set them equal to each other:

3x - 2 = -1/2x + 5


Some people don't like fractions, so to clear the fractions, multiply both sides by 2:
{{{2*3x - 2* 2 = 2*(-1/2)x + 2*5}}}

{{{6x - 4 = -x + 10}}}


Add +x from each side, and add +4 to each side to get all x terms to the left side and the number terms to the right side:
{{{6x +x  - 4 = -x + x + 10}}}

{{{7x - 4 =  10}}}

{{{7x - 4 + 4 =  10 + 4}}}

{{{ 7x = 14}}}
{{{ x = 14/7 = 2}}}


If {{{x = 2}}}, substitute into the first equation:  
{{{Y = 3x - 2}}}
{{{Y=3(2) - 2}}}
{{{Y = 6 - 2}}}
{{{Y = 4}}}


Check in the second equation:

Y=-1/2x + 5
{{{ 4 =(-1/2)*(2) + 5}}}

{{{ 4 = -1 + 5 }}}


R^2 at SCC