Question

Please help me solve question 2

Answer 1

(3, 6)

Explanation:

`\textsf{Equation 1}: \ y=\frac23x+4`

`\textsf{Equation 2}: \ 2x + 3y =24`

Substitute equation 1 into equation 2:

`\implies 2x + 3\left(\frac23x + 4 \right) =24`

Expand brackets:

`\implies 2x +2x+12=24`

Collect like terms:

`\implies 4x+12=24`

Subtract 12 from both sides:

`\implies 4x=12`

Divide both sides by 4:

`\implies x=3`

Now substitute found value of x into equation 1:

`\implies y=\frac23(3)+4`

`\implies y=2+4`

`\implies y=6`

Therefore, solution is (3, 6)

Answer 2

solution: ( 3 , 6 )

`\sf y =6`

`\sf x =3`

Explanation:

`\sf y = (2)/(3) x+4`

`\sf 2x+3y = 24`

make y the subject in equation 2:

`\sf 2x+3y = 24`

`\sf 3y = 24-2x`

`\sf y = (24-2x)/(3)`

insert this in equation 1:

`\sf (24-2x)/(3) =(2)/(3) x+4`

`\sf \sf (24-2x)/(3) =(2x+12)/(3)`

`\sf (24-2x) = (2x+12)`

`\sf -2x-2x=12-24`

`\sf -4x=-12`

`\sf x =3`

solve for y:

`\sf y = (24-2x)/(3)`

`\sf y = (24-2(3))/(3)`

`\sf y =6`