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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.

using the digits-9 to 9, without repeating any numbers, place a number in each box-example-1

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6 votes

Answer:

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}

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