Question

Solve the following using substitution: 3X = 6Y -94X + 3Y = -1

Answer 1

So we need to solve the following system of equations:

`\begin{gathered} 3x=6y-9 \\ 4x+3y=-1 \end{gathered}`

We must use the method of substitution. This means that the first step is to choose one of the equations and clear one of the variables, either x or y. So let's pick the first one and clear x:

`\begin{gathered} 3x=6y-9 \\ x=(6y-9)/(3) \\ x=2y-3 \end{gathered}`

Now we have an expression for x where x is a function of y. The next step is to take the right side of this expression and substitute the x on the second equation with it:

`\begin{gathered} 4x+3y=-1 \\ 4\cdot(2y-3)+3y=-1 \\ 8y-12+3y=-1 \end{gathered}`

Now we find y:

`\begin{gathered} 8y-12+3y=-1 \\ 11y-12=-1 \\ 11y=-1+12=11 \\ y=(11)/(11)=1 \end{gathered}`

Now we take the expression we find for x and substitute y=1 on it:

`\begin{gathered} x=2y-3=2\cdot1-3=2-3 \\ x=-1 \end{gathered}`

So the answer is:

`\begin{gathered} x=-1 \\ y=1 \end{gathered}`

Which is the point (-1,1) in the cartesian grid.