Solve Systems of Linear Equations by Graphing (Standard) (A) - Free Printable

Since I can’t view or process images directly, I’ll solve the Graphing Linear Systems (A) worksheet based on the equations you’ve typed out. The goal is to graph each system and identify its solution — which is the point where the two lines intersect.

I’ll solve all 4 systems algebraically (since graphing isn't possible here), but I’ll also explain how you would graph them and what the solution means.

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## 🔹 System 1:
Equations:
- \( 3x - y = 4 \)
- \( 7x + 2y = 18 \)

Step 1: Solve by substitution or elimination.

Let’s solve the first equation for \( y \):

From \( 3x - y = 4 \) →
\( y = 3x - 4 \)

Substitute into second equation:

\( 7x + 2(3x - 4) = 18 \)
→ \( 7x + 6x - 8 = 18 \)
→ \( 13x = 26 \)
→ \( x = 2 \)

Now plug back in:
\( y = 3(2) - 4 = 6 - 4 = 2 \)

✔ Solution: (2, 2)

Graphing Tip:

- For \( 3x - y = 4 \): When \( x=0 \), \( y=-4 \); when \( y=0 \), \( x=4/3 ≈ 1.33 \)
- For \( 7x + 2y = 18 \): When \( x=0 \), \( y=9 \); when \( y=0 \), \( x=18/7 ≈ 2.57 \)
- Plot both lines — they intersect at (2, 2)

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## 🔹 System 2:
Equations:
- \( x + y = 5 \)
- \( 2x + 7y = 0 \)

Step 1: Solve by substitution.

From first equation: \( x = 5 - y \)

Plug into second:

\( 2(5 - y) + 7y = 0 \)
→ \( 10 - 2y + 7y = 0 \)
→ \( 5y = -10 \)
→ \( y = -2 \)

Then \( x = 5 - (-2) = 7 \)

✔ Solution: (7, -2)

Graphing Tip:

- \( x + y = 5 \): Intercepts at (5,0) and (0,5)
- \( 2x + 7y = 0 \): Passes through origin; another point: if \( x=7 \), \( y=-2 \)
- Lines intersect at (7, -2)

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## 🔹 System 3:
Equations:
- \( 3x + 7y = 28 \)
- \( 6x + 7y = 49 \)

Step 1: Subtract equations to eliminate \( y \).

Eq2 – Eq1:
\( (6x + 7y) - (3x + 7y) = 49 - 28 \)
→ \( 3x = 21 \)
→ \( x = 7 \)

Plug into first equation:
\( 3(7) + 7y = 28 \)
→ \( 21 + 7y = 28 \)
→ \( 7y = 7 \)
→ \( y = 1 \)

✔ Solution: (7, 1)

Graphing Tip:

- First line: \( 3x + 7y = 28 \) → intercepts: (0, 4) and (28/3 ≈ 9.33, 0)
- Second line: \( 6x + 7y = 49 \) → intercepts: (0, 7) and (49/6 ≈ 8.17, 0)
- They intersect at (7,1)

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## 🔹 System 4:
Equations:
- \( y = 8 \) ← horizontal line
- \( 5x - y = 2 \)

Step 1: Plug \( y = 8 \) into second equation.

\( 5x - 8 = 2 \)
→ \( 5x = 10 \)
→ \( x = 2 \)

✔ Solution: (2, 8)

Graphing Tip:

- \( y = 8 \): Horizontal line through y=8
- \( 5x - y = 2 \) → rearrange: \( y = 5x - 2 \). Slope = 5, y-intercept = -2
- Intersection: at x=2, y=8 → (2,8)

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## ✔ Final Answers:

1. Solution: (2, 2)
2. Solution: (7, -2)
3. Solution: (7, 1)
4. Solution: (2, 8)

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## 📌 How to Graph Each System (for your worksheet):

For each problem:

1. Rewrite each equation in slope-intercept form (\( y = mx + b \)) if needed.
2. Plot two points per line (usually x- and y-intercepts).
3. Draw the lines carefully on the grid.
4. Mark the intersection point — that’s the solution!
5. Write the coordinates in the “Solution: (______)” box.

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Let me know if you’d like printable graph paper or step-by-step graphing instructions for any specific system!