Algebra 1 Solving Systems of Equations by Graphing Scaffolded ... - Free Printable

Let’s solve each system of equations step by step. We’ll graph them to find where the lines cross — that point is the solution!

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Problem 1:
Solve by graphing:
> y = 2x – 1
> y = –3x + 4

Step 1: Graph y = 2x – 1
- Start at (0, -1) — that’s the y-intercept.
- Slope is 2/1 → go up 2, right 1 → next point: (1, 1)
- Draw line through those points.

Step 2: Graph y = –3x + 4
- Start at (0, 4) — y-intercept.
- Slope is –3/1 → go down 3, right 1 → next point: (1, 1)
- Draw line.

Step 3: Find where they cross → looks like (1, 1)

Check: Plug x=1 into both equations:
y = 2(1) – 1 = 1 ✔
y = –3(1) + 4 = 1 ✔

✔ Solution: (1, 1)

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Problem 2:
Solve by graphing:
> y = –½x – 2
> y = –⁵₂x + 2

Step 1: Graph y = –½x – 2
- Start at (0, -2)
- Slope –½ → go down 1, right 2 → next point: (2, -3)
- Draw line.

Step 2: Graph y = –⁵⁄₂x + 2
- Start at (0, 2)
- Slope –⁵⁄₂ → go down 5, right 2 → next point: (2, -3)
- Draw line.

Step 3: They cross at (2, -3)

Check:
First equation: y = –½(2) – 2 = –1 – 2 = –3 ✔
Second: y = –⁵⁄₂(2) + 2 = –5 + 2 = –3 ✔

✔ Solution: (2, -3)

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Problem 3:
Solve the system:
> x + 2y = –2
> 3x + y = 4

We need to rewrite both in slope-intercept form (y = mx + b).

Eq 1: x + 2y = –2
→ 2y = –x – 2
→ y = –½x – 1

Eq 2: 3x + y = 4
→ y = –3x + 4

Now graph:

Graph y = –½x – 1
- Start at (0, -1)
- Down 1, right 2 → (2, -2)

Graph y = –3x + 4
- Start at (0, 4)
- Down 3, right 1 → (1, 1), then (2, -2)

They cross at (2, -2)

Check:
Plug into original equations:

Eq1: x + 2y = 2 + 2(-2) = 2 – 4 = –2 ✔
Eq2: 3x + y = 6 + (-2) = 4 ✔

✔ Solution: (2, -2)

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Problem 4:
Solve the system:
> 2x – y = –4
> x + 3y = –9

Rewrite both in slope-intercept form.

Eq1: 2x – y = –4
→ –y = –2x – 4
→ y = 2x + 4

Eq2: x + 3y = –9
→ 3y = –x – 9
→ y = –⅓x – 3

Graph:

y = 2x + 4
- Start at (0, 4)
- Up 2, right 1 → (1, 6)

y = –⅓x – 3
- Start at (0, -3)
- Down 1, right 3 → (3, -4)

Wait — let’s find intersection algebraically to be sure (since graphing might be tricky with fractions):

Set equal:
2x + 4 = –⅓x – 3

Multiply everything by 3 to eliminate fraction:
6x + 12 = –x – 9
6x + x = –9 – 12
7x = –21
x = –3

Plug back into y = 2x + 4:
y = 2(-3) + 4 = –6 + 4 = –2

Check in second equation:
x + 3y = –3 + 3(-2) = –3 – 6 = –9 ✔

✔ Solution: (–3, –2)

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Final Answer:
1. (1, 1)
2. (2, -3)
3. (2, -2)
4. (-3, -2)