Respuesta :

Answer:

The two equations are  y=x+4 and y=2x+5.

Step-by-step explanation:

Given that (-1,3) is solutions of the system of two linear equations.

Let y=mx + c be the generalized equation of line having slope m and y-intercept c.

For different values of m and c, there are corresponding linear equations.

As the lines are passing through the point (-1,3), so, pot x=-1 and y=3 in the generalized equation, we have

[tex]3=-1m+c \\\\\Rightarrow 3=-m+c \\\\\Rightarrow c-m=3\cdots(i).[/tex]

All the real values of c and m which satisfy equation (i) are the desired linear equations.

As we required only two linear equations, take any two values of c and m.

For c=4 and m=1 (satisfying equation (i))

[tex]y=1\times x +4 \\\\\Rightarrow y=x+4[/tex]

and for c=5, m=2

[tex]y=2\times x +5 \\\\\Rightarrow y=2x+5.[/tex]

Hence, the two equations are  y=x+4 and y=2x+5.

Ver imagen Ritz01
facundo3141592

We want to sketch a system of two linear equations such that the solution is (-1, 3). The graph can be seen at the end.

So basically, we just need to find two linear functions that pass through the point (-1, 3)

To get these, we can start with the general linear equation:

y = a*x + b

Then we define the value of b, for example, b = 0

y = a*x

now we force it to pass through the point (-1, 3)

3 = a*-1

3/-1 = a = -3

Then one of the linear equations is:

y = -3*x

To get the other, we do the same thing, this time with b = 2 (or any real number you want)

3 = a*-1 + 2

-1 = a

This gives the linear equation:

y = -1*x + 2

So the system is:

y = -1*x + 2

y = -3*x

The graph can be seen below:

If you want to learn more, you can read:

https://brainly.com/question/20067450

Ver imagen facundo3141592

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