Question 71964
Solve the system of equations by substitution:
1) {{{2x-3y = 7}}}
2) {{{y = 3x-7}}} Substitute this for y in equation 1) and solve for x.
1a) {{{2x-3(3x-7) = 7}}} Simplify and solve for x. Apply the distributive property.
{{{2x-9x+21 = 7}}} Notice the change of sign (- to +) on the last term! Now combine like-terms.
{{{-7x + 21 = 7}}} Subtract 21 from both sides.
{{{-7x = -14}}} Divide both sides by -7.
{{{x = 2}}} Now substitute this value of x into either one of the two original equations and solve for y. Using equation 2):
{{{y = 3(2)-7}}}
{{{y = 6-7}}}
{{{y = -1}}}
The solution is: (2, -1)
Here's the graph:
{{{graph(300,200,-5,5,-5,5,(2/3)x-(7/3),3x-7)}}}
Notice that the solution to this system of equations is the point of intersection of the two lines represented by the two equations.