"Solve by substitution"
color(blue)(13x+5y=16 (1st "equation")
color(blue)(x=4y+10 (2nd "equation")
"As we can see," x=4y+10,
"we can substitute it to the first equation"
rarr13(4y+10)+5y=16
"Use the distributive property -" color(brown)(a(b+c)=ab+ac
rarr(52y+130)+5y=16
rarr52y+130+5y=16
rarr57y+130=16
rarr57y=16-130
rarr57y=-114
rarrcolor(green)(y=-144/57=-2
"Now,substitute the value of y to the second equation"
rarrx=4(-2)+10
rarrx=-8+10
rarrcolor(green)(x=2
color(purple)({x,y=2,-2}