Question 171950
{{{x=y-7}}}, EQN 1 -------> {{{y=x+7}}}
{{{2x-5y=-2}}}, EQN 2 -----> {{{(2x+2)/5=y}}}
Subst. EQN 1 in EQN 2:
{{{2(y-7)-5y=-2}}}
{{{2y-14-5y=-2}}}
{{{-3y=-2+14=12}}} -------->{{{cross(-3)y/cross(-3)=cross(12)4/cross(-3)1}}} 
{{{highlight(y=-4)}}}
subst. in EQN 1:
{{{x=-4-7=highlight(-11)}}}
The lines intersect thru these points(-11,-4) as shown:
{{{drawing(300,300,-15,10,-10,10,graph(300,300,-15,10,-10,10,x+7,(2/5)x+(2/5)),circle(-11,-4,.20))}}} ---> RED Line, EQN 1; GREEN Line, EQN 2
.
{{{-3x+2y=10}}}, EQN 3 -------> {{{y=(3x+10)/2=(3/2)x+(10/2)}}}
{{{-2x-y=-5}}}, EQN 4 --------> {{{y=-2x+5}}}
We equate the 2 eqn's:
{{{-2x+5=(3/2)x+5}}}
{{{(3/2)x+2x=5-5}}}
{{{(3+6)x/2=0}}} -->{{{highlight(x=0)}}}
Subst {{{x=0}}} in EQN 4:
{{{-2(0)-y=-5}}} ------> {{{highlight(y=5)}}}
Therefore, these lines intersect at points(0,5), as we see:
{{{drawing(300,300,-10,10,-10,7,graph(300,300,-10,10,-10,7,(3/2)x+5,-2x+5),circle(0,5,.20)))}}}
-----> RED Line, EQN 3; GREEN Line, EQN 4
Thank you,
Jojo