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Solving a system of equations using substitution
y=3x+3
y=2x+8

~~~~~~~~~~
x+3y=17
2x+3y=22

Sagot :

naǫ
1.
[tex]y=3x+3 \\ y=2x+8 \\ \\ \hbox{substitute 3x+3 for y in the 2nd equation:} \\ 3x+3=2x+8 \\ 3x-2x=8-3 \\ x=5 \\ \\ y=2x+8=2 \times 5+8=10+8=18 \\ \\ \boxed{(x,y)=(5,18)}[/tex]

2.
[tex]x+3y=17 \\ 2x+3y=22 \\ \\ \hbox{solve the 1st equation for x:} \\ x+3y=17 \\ x=17-3y \\ \\ \hbox{substitute 17-3y for x in the 2nd equation:} \\ 2(17-3y)+3y=22 \\ 34-6y+3y=22 \\ -6y+3y=22-34 \\ -3y=-12 \\ y=\frac{-12}{-3} \\ y=4 \\ \\ x=17-3y=17-3 \times 4=17-12=5 \\ \\ \boxed{(x,y)=(5,4)}[/tex]
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