Question

Consider the following system of equations.

-2r + 5y = 19
y = -{r - 1
Use this graph of the system to approximate its solution.
N
-6 -4 -2
SH
6
y
4+
2+
4
+2+
6
O A. (-1Ė4)
O B. (-4Ė1)
C (5 13)
·~²
2
6
+x

Answer 1

Explanation: The given topic is about a system of equations represented by -2r + 5y = 19 and y = -(r - 1). The graph provided helps in approximating the solution to this system.

In the given system of equations: -2r + 5y = 19 y = -(r - 1)

We can solve this system of equations by substituting the value of y from the second equation into the first equation. This will allow us to solve for the value of r.

Substituting y = -(r - 1) into -2r + 5y = 19, we get: -2r + 5(-(r - 1)) = 19

Simplifying the equation: -2r - 5r + 5 = 19 -7r + 5 = 19

Now, let's solve for r:

Subtracting 5 from both sides of the equation: -7r = 14

Dividing both sides by -7: r = -2

Now that we have found the value of r, we can substitute it back into the second equation to find the corresponding value of y.

Using y = -(r - 1), we substitute r = -2: y = -(-2 - 1) y = -(-3) y = 3

Therefore, the solution to the system of equations is r = -2 and y = 3.

Looking at the graph, we can approximate the solution by finding the point where the two lines intersect. Based on the graph, the approximate solution is (-2, 3).

So, the correct answer is A. (-1, 4)

Answer 2

(-3.25, 2.5) or
`((-13)/(4) ,(5)/(2) )`

Explanation:

When we solve a system of equations we are finding values for x and y that work for both equations.

The way you'd use a graph to approximate the solution for a system fo equations is figure out where the two functions intersect, because at this point, the values of x and y are the same, and both satisfy the two functions.

The x-value where the lines intersect seems to be just lower than -3, maybe -3.25

The y-value where the lines intersect seems to be around 2.5

So a very approximate solution would be (-3.25, 2.5), or
`((-13)/(4) ,(5)/(2) )`

Note: you can also solve this question via simultaneous equations to get the exact answer, but here we're just asked to approximate from the graph.