Question 170288
Solve the system:
1) {{{2(x-y) = 3+x}}} and
2) {{{x = 3y+4}}}
The idea behind the "elimination" or "substitution" method is to reduce the problem from two equations with two unknowns (variables) to one equation with one unknown.  This is accomplished by "eliminating" one of the unknowns.
In this problem, you can conveniently substitute the x in the first equation with the x in the second equation, thus eliminating the x-variable.
It would be simpler to first simplify the first equation as you have started to do.
1) {{{2(x-y) = 3+x}}}
{{{2x-2y = 3+x}}} Subtract x from both sides.
{{{x-2y = 3}}} Now substitute the x from equation 2)
{{{(3y+4)-2y = 3}}} Simplfy and solve for y. Combine like-terms.
{{{y+4 = 3}}} Subtract 4 from both sides.
{{{y = -1}}} Now substitute this value of y into equation 2) and solve for x.
{{{x = 3y+4}}} Substitute y = -1
{{{x = 3(-1)+4}}}
{{{x = 1}}} So the solution is: (1, -1) and the solution shows the point of intersection of the two lines represented by the two linear equations.
{{{graph(400,400,-5,5,-3,3,(1/2)x-3/2,(1/3)x-4/3)}}}