Respuesta :
[tex]\begin{gathered} 3x+2y=12 \\ x=\frac{2}{3}y \end{gathered}[/tex]
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.
[tex]\begin{gathered} 3x+2y=12 \\ 3(\frac{2}{3}y)+2y=12 \end{gathered}[/tex]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)
[tex]\begin{gathered} 2y+2y=12 \\ \text{Add similar terms.} \\ 4y=12 \\ \text{Divide both sides of the equation by 4.} \\ \frac{4y}{4}=\frac{12}{4} \\ y=3 \end{gathered}[/tex]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.
[tex]\begin{gathered} x=\frac{2}{3}y \\ x=\frac{2}{3}(3) \\ x=2 \end{gathered}[/tex]The value of x = 2.
To check whether these values are true for both equations, we can plug them in.
[tex]\begin{gathered} 3x+2y=12 \\ 3(2)+2(3)=12_{} \\ 6+6=12 \\ 12=12 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{2}{3}y \\ 2=\frac{2}{3}(3) \\ 2=\frac{6}{3} \\ 2=2 \end{gathered}[/tex]Indeed, the values of x and y are true to both equations. The solution x = 2, y = 3 correct.
