Answer:
a) i) y = - 5/3
ii) y = 4/3
b) i) x = 1
ii) x = -3/4
Step-by-step explanation:
[tex]y=\dfrac23x +\dfrac13[/tex]
a) i) [tex]x=-3[/tex]
[tex]\implies y=\dfrac23(-3) +\dfrac13\\\\\\\implies y=\dfrac{-6}{3} +\dfrac13\\\\\\\implies y=\dfrac{1-6}{3} \\\\\\\implies y=-\dfrac53[/tex]
ii) [tex]x=1\frac12=\dfrac32[/tex]
[tex]\implies y=\dfrac23\left(\dfrac32\right) +\dfrac13\\\\\\\implies y=\dfrac{6}{6}+\dfrac13\\\\\\\implies y=\dfrac{3}{3}+\dfrac13\\\\\\\implies y=\dfrac{3+1}{3}\\\\\\\implies y=\dfrac43[/tex]
b) i) [tex]y=1[/tex]
[tex]\implies \dfrac23x +\dfrac13=1\\\\\\\implies \dfrac23x =1-\dfrac13\\\\\\\implies \dfrac23x =\dfrac23\\\\\\\implies x =1[/tex]
ii) [tex]y=-\dfrac16[/tex]
[tex]\implies \dfrac23x +\dfrac13=-\dfrac16\\\\\\\implies \dfrac23x =-\dfrac12\\\\\\\implies x =-\dfrac12 \div \dfrac23=-\dfrac12 \times\dfrac32=-\dfrac34[/tex]
