Question

20. Find a solution to the following system of equations.

-3x + 3y = -9
-3x+y=7
O
O
O
(5,2)
(-5, -8)
(-2,2)

Answer 1

To find a solution to the system of equations, we can use the elimination method, which involves adding or subtracting the equations to eliminate one of the variables. Here are the steps:

`\begin{align}</p><p>-3x + 3y &= -9 \</p><p>-3x + y &= 7 \</p><p>\end{align}`

We can eliminate $x$ by subtracting the second equation from the first equation:

`\begin{align}</p><p>-3x + 3y &= -9 \</p><p>(-3x + y &= 7) \</p><p>\end{align}`

This gives us:

`\begin{align}</p><p>4y &= -16 \</p><p>y &= -4 \</p><p>\end{align}`

Now, we can use the second equation to solve for $x$:

`\begin{align}</p><p>-3x + y &= 7 \</p><p>-3x + (-4) &= 7 \</p><p>-3x &= 11 \</p><p>x &= -(11)/(3) \</p><p>\end{align}`

So the solution to the system of equations is $\boxed{(-\frac{11}{3}, -4)}$.

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