Question

using the digits-9 to 9, without repeating any numbers, place a number in each box to create a system of equations that has a solution and quadrant 2 tip: in quadrant 2, the x-coordinate is negative and the y - coordinate is positive.

Answer 1

Our system of equations is:

`\begin{cases}4x+5y={1} \\ y={2x+3}\end{cases}`

And its solution is:

`\begin{gathered} x=-1 \\ y=1 \end{gathered}`

Explanation:

First, we'll fill out the second equation.

We'll choose a value for x. In this case, we'll work with:

`x=-1`

Now, we'll chose 2 as a coefficient for x and 3 as the independent term. This way, we'll have the equation:

`y=2x+3`

And since we've established that x = 1,

`\begin{gathered} y=2(-1)+3 \\ \rightarrow y=1 \end{gathered}`

From now on, we know that the solution to our system is:

`\begin{gathered} x=-1 \\ y=1 \end{gathered}`

Now, we'll work on the first equation. We'll chose 4 as a coefficient for x and 5 as a coefficient for y. This way, we'll have the expression:

`4x+5y`

And since we already know the values of x and y, we'll have that:

`4x+5y\rightarrow4(-1)+5(1)\rightarrow1`

Therefore, our first equation is:

`4x+5y=1`

Therefore, we can conclude that our system of equations is:

`\begin{cases}4x+5y={1} \\ y={2x+3}\end{cases}`

And its solution is:

`\begin{gathered} x=-1 \\ y=1 \end{gathered}`