Question

I need help type the correct answer in each box find a solution for this system of equations 2X plus 4Y equals 8X equals three why take away six

Answer 1

The solution to the system of equations is;

`\begin{gathered} x=0 \\ y=2 \end{gathered}`

Step-by-step explanation:

Given the system of equations;

`\begin{gathered} 2x+4y=8\text{ ----------1} \\ x=3y-6 \\ x-3y=-6\text{ ----------2} \end{gathered}`

Multiplying equation 2 by 2 and subtracting from equation 1;

`\begin{gathered} x-3y=-6 \\ * \\ 2 \\ = \\ 2x-6y=-12\text{ -----------2.1} \end{gathered}`
`\begin{gathered} 2x+4y=8\text{ ----------1} \\ - \\ 2x-6y=-12\text{ -----------2.1} \\ = \\ 0+10y=20 \\ 10y=20 \\ y=(20)/(10) \\ y=2 \end{gathered}`

We can then substitute the value of y into equation 1, to get x;

`\begin{gathered} 2x+4y=8 \\ 2x+4(2)=8 \\ 2x=8-8 \\ 2x=0 \\ x=0 \end{gathered}`

Therefore, the solution to the system of equations is;

`\begin{gathered} x=0 \\ y=2 \end{gathered}`