Question 428899
2x+3y=8	.............1	
x-5y=17	.............2	
	
Eliminate y							
multiply (1)by 	5						
Multiply (2) by 3						
10x+5y=40		
3x+2y=51		
								
Add the two equations								
								
13x=91		
								
/13							
								
x=7		
								
plug value of x	in (1)				
								
2x+3y=8		
14+3y=8		
3y=8+-14
3y=-6		
y=-2

(7,-2) is the solution.

2x+3y=8	.............1	
x=0 , y=8/3 ( 0,8/3)
y=0, x=4 (4,0)

x-5y=17	.............2	
x=0,y=-17/5 (0,-17/5)
y=0,x=17 (17,0)

Plot two points generated from each equation (1) & (2) draw the line graph

{{{drawing(300,300,-10,20,-10,10,grid(2),circle(0,8/3,0.4),circle(4,0,0.4),circle(0,-17/5,0.4),circle(17,0,0.4),circle(7,-2,0.4),graph(300,300,-10,20,-10,10,y=(-2x/3)+8/3,y=(x/5)-17/5))}}}

The intersection is the solution