It looks like you've uploaded a worksheet titled
"Solving Linear Systems by Graphing", which contains 9 systems of linear equations. Each system has two equations, and the goal is to
solve each system by graphing — that is, graph both lines on the provided coordinate plane and find their point of intersection, which represents the solution.
However, since I can't view images directly, I’ll need you to
describe or type out the equations for each problem (1 through 9) so I can help you solve them step-by-step.
But here’s how we’d approach this in general:
---
🔍 How to Solve a System of Linear Equations by Graphing:
For each pair of equations:
1.
Rewrite each equation in slope-intercept form:
$ y = mx + b $
2.
Graph both lines on the same coordinate grid.
3.
Find the point where the lines intersect.
4. That point $(x, y)$ is the
solution to the system.
If the lines are parallel → no solution (inconsistent).
If the lines are the same → infinitely many solutions (dependent).
---
✔ Example (if one of the problems was):
> Problem 1:
> $ y = x + 3 $
> $ y = -x + 1 $
Step 1: Both are already in slope-intercept form.
- Line 1: slope = 1, y-intercept = 3
- Line 2: slope = -1, y-intercept = 1
Step 2: Graph both lines.
Step 3: Find intersection.
Set equations equal:
$ x + 3 = -x + 1 $
$ 2x = -2 $ → $ x = -1 $
Plug back: $ y = (-1) + 3 = 2 $
Solution: $ (-1, 2) $
---
Please provide the actual equations from the image (e.g., list all 9 problems), and I’ll walk you through solving each one with explanations and graphs described in words.
Parent Tip: Review the logic above to help your child master the concept of linear equation graphs worksheet.
