How do you solve the system #13x + 5y = 16# and #x = 4y + 10#?

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Answer 1 · 2016-07-09T06:55:14

#color(purple)({x,y=2,-2}#

#"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}#