Question

Please solve in the substitution method only 3x + 2y = 12x = 2/3 y

Answer 1

`\begin{gathered} 3x+2y=12 \\ x=(2)/(3)y \end{gathered}`

To solve the system of equation using substitution method only, here are the steps.

1. Since the 2nd equation has been equated already into x = or y = , we can use this value to substitute the "x" value in the first equation.

`\begin{gathered} 3x+2y=12 \\ 3((2)/(3)y)+2y=12 \end{gathered}`

2. Then, solve for y.

a. Eliminate first the parenthesis by multiplying the number outside it to the number inside it. (3 x 2/3y = 2y)

`\begin{gathered} 2y+2y=12 \\ \text{Add similar terms.} \\ 4y=12 \\ \text{Divide both sides of the equation by 4.} \\ (4y)/(4)=(12)/(4) \\ y=3 \end{gathered}`

Therefore, the value of y is 3.

3. Plug in the value of "y" to either of the equation to solve for x. For this solution, we will plug it in to the second equation.

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

The value of x = 2.

To check whether these values are true for both equations, we can plug them in.

`\begin{gathered} 3x+2y=12 \\ 3(2)+2(3)=12_{} \\ 6+6=12 \\ 12=12 \end{gathered}`
`\begin{gathered} x=(2)/(3)y \\ 2=(2)/(3)(3) \\ 2=(6)/(3) \\ 2=2 \end{gathered}`

Indeed, the values of x and y are true to both equations. The solution x = 2, y = 3 correct.