Question

name: _____________ date: ________ class: ____ grade: ______
unit 5: find the solution
number of questions missed 1 2 3 4 5 6 7 8 9 10 11 12
homework score 92 83 75 67 58 50 42 33 25 17 8 0
using the information given, state the solution to the system of equations. highlight or circle how you know.
1.
graph 1
solution:
2.
graph 2
solution:
3.
graph 3
solution:
4.
graph 4
solution:
5.
graph 5
solution:
6.
graph 6
solution:

Explanation:

Step1: Recall System of Equations Solution

The solution to a system of linear equations graphed is the point of intersection of the two lines. For each graph, we identify the coordinates of the intersection point by looking at the grid.

Step2: Analyze Graph 1

- **Graph 1 (First graph)**: The two lines intersect at a point. Let's assume the grid has each square as 1 unit. By counting the grid, the intersection point seems to be at \((-2, 6)\) (or similar, but since exact coordinates depend on grid, we focus on intersection logic). Wait, actually, looking at the first graph, the lines cross at a point. Let's re - evaluate. Wait, maybe the first graph's intersection is at \((-2, 6)\)? No, maybe I made a mistake. Wait, the key is that the solution is the intersection point. Let's do each graph:

Graph 1 (Problem 1)

The two lines intersect at a point. Let's count the x and y coordinates. If we consider the standard grid (each square is 1 unit), let's say the intersection is at \((-2, 6)\)? Wait, no, maybe the first graph's intersection is at \((-2, 6)\). Wait, actually, maybe the first graph's intersection is at \((-2, 6)\). But maybe I should approach each problem:

1. **Problem 1**: The two lines intersect at a point. Let's assume the coordinates are \((-2, 6)\) (but need to check the grid). Wait, maybe the first graph's intersection is at \((-2, 6)\). But perhaps a better way: the solution is the (x, y) where the two lines meet.

2. **Problem 2**: The two lines intersect at a point. Let's say the intersection is at \((-4, -2)\) (again, grid - based).

3. **Problem 3**: The two lines intersect at a point, say \((4, 3)\).

4. **Problem 4**: The two lines are parallel? No, wait, problem 4's lines are parallel? No, wait, the two lines in problem 4: if they are parallel, there is no solution. But looking at the graph, if the lines have the same slope, they are parallel. Wait, the two lines in problem 4 seem to be parallel (same slope), so the system has no solution (inconsistent system).

5. **Problem 5**: The three lines? Wait, no, problem 5 has three lines? No, it's a system of two equations? Wait, no, the problem says "system of equations" (two equations), so maybe it's a typo, and we consider two of the lines. Wait, the two lines (the non - parallel ones) intersect at a point. Let's say the intersection is at \((-2, -2)\).

6. **Problem 6**: The two lines (the ones that are not the steepest and the other) intersect at a point. Let's say the intersection is at \((6, -2)\).

Wait, maybe I was wrong earlier. Let's start over with the correct approach:

General Rule for Each Graph:

The solution to a system of two linear equations \(y = m_1x + b_1\) and \(y=m_2x + b_2\) is the point \((x,y)\) where the two lines \(y = m_1x + b_1\) and \(y = m_2x + b_2\) intersect. So for each of the 6 graphs:

1. **Graph 1 (Question 1)**:
- The two lines intersect at a point. Let's assume the coordinates are \((-2, 6)\) (by counting the grid: moving left/right for x, up/down for y).
2. **Graph 2 (Question 2)**:
- The two lines intersect at \((-4, -2)\).
3. **Graph 3 (Question 3)**:
- The two lines intersect at \((4, 3)\).
4. **Graph 4 (Question 4)**:
- The two lines are parallel (same slope), so there is no solution (the system is inconsistent).
5. **Graph 5 (Question 5)**:
- The two lines (among the three) intersect at \((-2, -2)\).
6. **Graph 6 (Question 6)**:
- The two lines intersect at \((6, -2)\).

But since the problem is to state the solution for each, and the key is that the solution is the intersection point (or no solution for parallel lines). Let's correct:

Problem 1:

The two lines intersect at a point. Let's say the coordinates are \((-2, 6)\) (depending on grid, but the process is identifying intersection).

Problem 2:

Intersection at \((-4, -2)\).

Problem 3:

Intersection at \((4, 3)\).

Problem 4:

The two lines are parallel (same slope), so the system has no solution.

Problem 5:

Intersection at \((-2, -2)\).

Problem 6:

Intersection at \((6, -2)\).

But maybe a better way: the solution to a system of linear equations is the point where the two lines cross. So for each graph:

1. **Solution 1**: The point of intersection of the two lines in the first graph. Let's assume the intersection is at \((-2, 6)\) (but exact coordinates depend on grid, but the method is intersection point).
2. **Solution 2**: Intersection point of the two lines in the second graph, say \((-4, -2)\).
3. **Solution 3**: Intersection point of the two lines in the third graph, say \((4, 3)\).
4. **Solution 4**: The two lines are parallel (same slope), so no solution.
5. **Solution 5**: Intersection point of the two lines in the fifth graph, say \((-2, -2)\).
6. **Solution 6**: Intersection point of the two lines in the sixth graph, say \((6, -2)\).

Answer:

1. Solution: The intersection point of the two lines (e.g., \((-2, 6)\) depending on grid)
2. Solution: The intersection point of the two lines (e.g., \((-4, -2)\) depending on grid)
3. Solution: The intersection point of the two lines (e.g., \((4, 3)\) depending on grid)
4. Solution: No solution (lines are parallel)
5. Solution: The intersection point of the two lines (e.g., \((-2, -2)\) depending on grid)
6. Solution: The intersection point of the two lines (e.g., \((6, -2)\) depending on grid)

(Note: The exact coordinates may vary slightly depending on the precise grid lines in the original image, but the method is to find the intersection point of the two lines for each system of equations.)