Question

System: 3x+2y=6 x-y=-3 find the value for x. find the value for y.

Answer 1

Given a system of equations:

`\begin{gathered} 3x+2y=6 \\ x-y=-3 \end{gathered}`

We have to solve the system of equations.

We can solve this system of equations using the substitution method.

From the second equation, we have x - y = -3, which implies that x = y - 3. Substitute x = y - 3 in the first equation:

`\begin{gathered} 3(y-3)+2y=6 \\ 3y-9+2y=6 \\ 5y=6+9 \\ 5y=15 \\ y=(15)/(5) \\ y=3 \end{gathered}`

Now, we have y = 3, put in x = y - 3 to get,

`\begin{gathered} x=3-3 \\ x=0 \end{gathered}`

Thus, the solution of the system of equations is (0, 3).