1 what is the x value of the following system of equations?
y = -4
x = y + 1
2 what is the y value of the following system of equations?
x = 3
y = x - 5
3 what are the x and y values to the solution of the system of equations?
(image of a graph with lines intersecting)
4 how many solutions does this system of equations have?
(image of a graph with lines)
5 use substitution to solve this system of equations.
y = x + 6
2x + y = -3
6 what is the y value of the solution to the system of equations?
2x - 3y = -11
2x + y = 9

Question

Accepted Answer

### Question 1
# Explanation:
## Step1: Substitute $ y = -4 $ into $ x = y + 1 $
$ x = -4 + 1 $
## Step2: Calculate the value of $ x $
$ x = -3 $
# Answer:
$ x = -3 $

### Question 2
# Explanation:
## Step1: Substitute $ x = 3 $ into $ y = x - 5 $
$ y = 3 - 5 $
## Step2: Calculate the value of $ y $
$ y = -2 $
# Answer:
$ y = -2 $

### Question 3
(Assuming the intersection point from the graph: looking at the graph, the intersection seems to be at $ x = 0 $, $ y = -5 $ (approximate from the grid, but need to check the lines. Wait, the dark line and the vertical line? Wait, maybe the intersection is where the two lines cross. Wait, the graph has two lines intersecting? Wait, no, three lines? Wait, maybe the solution is the point where all three? No, system of equations is two lines. Wait, the graph for question 3: the dark line and the other line? Wait, maybe the intersection is at $ x = 0 $, $ y = -5 $? Wait, maybe the coordinates are $ x = 0 $, $ y = -5 $ (since the vertical line is at x=0, and the dark line crosses it at y=-5? Or maybe the intersection of the two non-vertical lines? Wait, maybe the answer is $ x = 0 $, $ y = -5 $ (but need to confirm. Alternatively, maybe the lines intersect at (0, -5). So:
# Explanation:
From the graph, the two lines (or the relevant lines) intersect at $ x = 0 $ and $ y = -5 $ (by observing the grid: x=0, y=-5 is the intersection point).
# Answer:
$ x = 0 $, $ y = -5 $

### Question 4
# Explanation:
The two lines in the graph are parallel? Wait, no, the two lines have the same slope? Wait, the graph shows two lines that are parallel? No, wait, the lines look like they are parallel? Wait, no, if two lines are parallel, they have no solution. Wait, the graph for question 4: the two lines are parallel? Wait, the lines have the same slope, so they are parallel and never intersect. So the system has no solution? Wait, no, wait, the lines in the graph: are they parallel? Let's see, the two lines have the same slope, so they are parallel, so the system has 0 solutions.
## Step1: Analyze the lines' slopes
The two lines in the graph have the same slope (they are parallel), so they never intersect.
## Step2: Determine the number of solutions
A system of linear equations with parallel lines (same slope, different y-intercepts) has no solution.
# Answer:
0 solutions

### Question 5
# Explanation:
## Step1: Substitute $ y = x + 6 $ into $ 2x + y = -3 $
$ 2x + (x + 6) = -3 $
## Step2: Simplify the equation
$ 2x + x + 6 = -3 $
$ 3x + 6 = -3 $
## Step3: Subtract 6 from both sides
$ 3x = -3 - 6 $
$ 3x = -9 $
## Step4: Divide by 3
$ x = -3 $
## Step5: Substitute $ x = -3 $ into $ y = x + 6 $
$ y = -3 + 6 $
$ y = 3 $
# Answer:
$ x = -3 $, $ y = 3 $

### Question 6
# Explanation:
We have the system:
$ 2x - 3y = -11 $
$ 2x + y = 9 $
## Step1: Subtract the second equation from the first to eliminate $ x $
$ (2x - 3y) - (2x + y) = -11 - 9 $
## Step2: Simplify
$ 2x - 3y - 2x - y = -20 $
$ -4y = -20 $
## Step3: Solve for $ y $
$ y = \frac{-20}{-4} = 5 $
# Answer:
$ y = 5 $

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QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Substitute \( y = -4 \) into \( x = y + 1 \)

Step2: Calculate the value of \( x \)

Step1: Substitute \( x = 3 \) into \( y = x - 5 \)

Step2: Calculate the value of \( y \)

Answer:

Question 2