Question

Solve the following using substitution: 3X = 6Y -44X + 3Y = -1

Answer 1

x = -6/11 and y = 13/33

1) Let's solve this by the Substitution Method:

3x =6y -4

4x +3y =-1

Rewriting the 1st equation we have:

`\begin{gathered} x=(6y)/(3)-(4)/(3) \\ x=2y-(4)/(3) \end{gathered}`

2) Let's now plug into the 2nd equation the value of x:

`\begin{gathered} 4x+3y=-1 \\ 4((6y)/(3)-(4)/(3))+3y=-1 \\ 8y-(16)/(3)+3y=-1 \\ 11y=-1+(16)/(3) \\ 11y=(13)/(3) \\ y=(13)/(3)\cdot(1)/(11) \\ y=(13)/(33) \end{gathered}`

2.2) Now, let's plug the quantity of y we've just found into the 1st Equation:

`\begin{gathered} 3x=6((13)/(33))-4 \\ 3x=(78)/(33)-4 \\ 3x=-(18)/(11)\text{ }*(1)/(3) \\ x=-(6)/(11) \end{gathered}`

Note that we've simplified the final result.

3) Hence, the answer is:

x = -6/11 and y = 13/33