Question 73146
Set the two equations equal to each other. Since they both equal y, they both equal each other. For instance if we have y=x and y=5, then x=5 since we can substitute 5 into y. 
Substitute {{{y=highlight(-6+2x)}}} into {{{highlight(y)=(3/2)x+4}}}
{{{highlight(-6+2x)=(3/2)x+4}}}Now we have everything in terms of x. Solve for x.
{{{2x=(3/2)x+4+6}}}Add 6 to both sides
{{{2x-(3/2)x=10}}}Subtract 3/2x from both sides
{{{(1/2)x=10}}}Multiply both sides by 2
{{{x=20}}}
Substitute this back into {{{y=(3/2)x+4}}}
{{{y=(3/2)(20)+4}}}
{{{y=3*10+4}}}
{{{y=34}}}
Check:
{{{y=-6+2x}}}Use this first
{{{34=-6+2*20}}}
{{{34=-6+40}}}
{{{34=34}}}Works
{{{34=(3/2)x+4}}}Next use this equation to check
{{{34=(3/2)(20)+4}}}
{{{34=3*10+4}}}
{{{34=34}}}Works
<p>
So the intersection is (20,34)