8th-grade-math-solving-systems-by-graphing - Free Printable

Let’s solve each system of equations by graphing. That means we’ll draw both lines on the same coordinate plane and find where they cross — that point is the solution.

We’ll go one problem at a time.

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Problem 1:
Equations:
- y = 2x – 4
- y = –3x + 1

Step 1: Graph y = 2x – 4
This line has slope 2 (rise 2, run 1) and y-intercept –4.
Start at (0, –4). From there, go up 2, right 1 → (1, –2), then (2, 0), etc.

Step 2: Graph y = –3x + 1
Slope is –3 (down 3, right 1), y-intercept is 1.
Start at (0, 1). Go down 3, right 1 → (1, –2), then (2, –5), etc.

Wait — both lines pass through (1, –2)? Let’s check:

For y = 2x – 4: plug in x=1 → y = 2(1) – 4 = –2 ✔️
For y = –3x + 1: plug in x=1 → y = –3(1) + 1 = –2 ✔️

So they intersect at (1, –2).

✔ Solution for #1: (1, –2)

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Problem 2:
Equations:
- y = –x + 3
- y = –5x – 1

Step 1: Graph y = –x + 3
Slope = –1, y-intercept = 3 → start at (0, 3), go down 1, right 1 → (1, 2), (2, 1), etc.

Step 2: Graph y = –5x – 1
Slope = –5 (steep!), y-intercept = –1 → start at (0, –1), go down 5, right 1 → (1, –6)

But let’s find where they meet algebraically to be sure (since graphing might be tricky with steep slopes):

Set them equal:
–x + 3 = –5x – 1
Add 5x to both sides: 4x + 3 = –1
Subtract 3: 4x = –4
Divide by 4: x = –1

Now plug x = –1 into either equation:
y = –(–1) + 3 = 1 + 3 = 4
Check other: y = –5(–1) –1 = 5 –1 = 4 ✔️

So intersection at (–1, 4)

✔ Solution for #2: (–1, 4)

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Problem 3:
Equations:
- y = –8x + 4
- y = –x – 3

Set equal:
–8x + 4 = –x – 3
Add 8x to both sides: 4 = 7x – 3
Add 3: 7 = 7x
x = 1

Plug into y = –x – 3 → y = –1 – 3 = –4
Check other: y = –8(1) + 4 = –4 ✔️

✔ Solution for #3: (1, –4)

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Problem 4:
Equations:
- y = –6x – 3
- y = –x + 2

Set equal:
–6x – 3 = –x + 2
Add 6x: –3 = 5x + 2
Subtract 2: –5 = 5x
x = –1

Plug into y = –x + 2 → y = –(–1) + 2 = 1 + 2 = 3
Check other: y = –6(–1) –3 = 6 –3 = 3 ✔️

✔ Solution for #4: (–1, 3)

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Final Answer:
1) (1, –2)
2) (–1, 4)
3) (1, –4)
4) (–1, 3)