8th Grade Math Worksheets - Math in Demand - Free Printable

Let’s go through each problem one by one. We’re looking at systems of equations and how many solutions they have — based on graphs or descriptions.

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Problem 1:
We see two lines on the graph. They are parallel (same slope) but not the same line — they never cross.
→ Parallel lines = no solution.
Answer: B) No Solution

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Problem 2:
The graph shows two lines that cross at exactly one point.
Also, the equations given are y = -x and -y = x → which is the same as y = -x. Wait — actually, if you rearrange -y = x, you get y = -x. So both equations are the SAME line!
Wait — let me double-check:
Equation 1: y = -x
Equation 2: -y = x → multiply both sides by -1 → y = -x
So yes — identical lines → infinitely many solutions.
But wait — look at the graph! The graph shows two different lines crossing? Hmm… maybe I misread.

Actually, looking again — in Problem 2, the graph has two lines: one going down from left to right (slope -1), and another also going down but steeper? Wait — no, let’s read the labels.

It says: “y = -x” and “-y = x”. But -y = x is the same as y = -x. So it’s the same equation twice → same line → infinite solutions.

BUT — the graph might be misleading? Or maybe it’s a trick? Let’s trust the algebra.

If two equations are identical → infinitely many solutions.

Answer: F) Infinitely Many Solutions

Wait — hold on. Let me check the graph again visually. In box 2, there are two lines drawn — one labeled y=-x, and another labeled -y=x. But since -y=x is equivalent to y=-x, they should be the same line. If the graph shows them as overlapping, then F. If they’re drawn as different, maybe it’s an error? But according to math, they are the same.

I think we go with the math: same equation → infinite solutions.

Answer: F

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Problem 3:
Graph shows two lines crossing at one point → one solution.
Answer: G) One Solution

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Problem 4:
Two lines — one straight, one curved? Wait — no, both look like straight lines. Are they parallel? Let’s see — one goes down steeply, the other less steep? Actually, looking closely — they intersect at one point? Or are they parallel?

Wait — in box 4, the top line is decreasing slowly, bottom line decreasing faster — they will cross somewhere off-screen? But in the visible grid, they don’t cross — but that doesn’t mean they never cross.

Actually, unless they are parallel, they will cross eventually. Are they parallel? Slopes look different — so they must cross at one point → one solution.

Wait — but let’s think: if two lines have different slopes, they always intersect once → one solution.

Unless they are parallel (same slope) → no solution.

Or same line → infinite.

In this case, slopes are different → one solution.

Answer: J) One Solution

Wait — but looking at the graph again — the top line is almost flat, bottom line is steep — definitely different slopes → must cross → one solution.

Yes.

Answer: J

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Problem 5:
“Two equations that have the same slope will have:”

Same slope → could be parallel (no solution) OR same line (infinite solutions). But the question doesn’t say anything about intercepts.

But typically, if only slope is mentioned and nothing else, we assume they are not the same line — so parallel → no solution.

But wait — option M is “No Solution”, N is “One Solution”, O is “Infinitely Many”.

If two lines have same slope, they are either parallel (no solution) or coincident (infinite). Since the question doesn’t specify, but in multiple choice, and given context, probably expecting “no solution” for same slope different intercept.

But let’s see the options — M is “No Solution” — that’s likely correct if we assume different y-intercepts.

Actually, standard teaching: same slope, different intercept → no solution.

Same slope, same intercept → infinite.

Since it just says “same slope”, without mentioning intercept, but in most worksheets, they imply different lines → no solution.

Answer: M) No Solution

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Problem 6:
“Two equations that cross at a point because they do not have the same slope and are not identical equations will have:”

Cross at a point → one solution.

Not same slope → guaranteed to cross once.

Not identical → not infinite.

So → one solution.

Answer: P) One Solution

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Problem 7:
“Two equations that are identical equations will have:”

Identical → same line → every point is a solution → infinitely many.

Answer: U) Infinitely Many Solutions

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Now, let’s match answers to bubbles:

Problem 1: B
Problem 2: F
Problem 3: G
Problem 4: J
Problem 5: M
Problem 6: P
Problem 7: U

Now bubble sheet:

For #1: B → second row, first column → OB
#2: F → sixth row, first column → OF
#3: G → seventh row, first column → OG
#4: J → fourth row, second column → OJ
#5: M → fifth row, third column → OM
#6: P → sixth row, third column → OP
#7: U → seventh row, third column → OU

Wait — let’s map properly.

Bubble sheet layout:

Row 1: OA OH OO
Row 2: OB OI OP
Row 3: OC OJ OQ
Row 4: OD OK OR
Row 5: OE OL OS
Row 6: OF OM OT
Row 7: OG ON OU

So:

#1: B → Row 2, Col 1 → OB
#2: F → Row 6, Col 1 → OF
#3: G → Row 7, Col 1 → OG
#4: J → Row 3, Col 2 → OJ
#5: M → Row 6, Col 2 → OM
#6: P → Row 2, Col 3 → OP
#7: U → Row 7, Col 3 → OU

So bubbled answers:

OB, OF, OG, OJ, OM, OP, OU

But the instruction says: “Bubble in your answers below for problems #1-7.”

And the bubble sheet has letters A-U arranged in columns.

Final Answer should list the choices for each problem, and perhaps the bubbled version? But since the user didn’t ask to fill bubbles, just solve, I’ll give the letter answers per problem.

But to be precise, let’s output the answers as requested.

Final Answer:

1. B
2. F
3. G
4. J
5. M
6. P
7. U

And for bubbling: OB, OF, OG, OJ, OM, OP, OU — but since the question didn’t explicitly ask to report bubbled format, and the main task is to determine number of solutions, I’ll stick to the letter choices.

Actually, re-reading directions: “Make sure to bubble in your answers below on each page so that you can check your work.” — but since we’re not filling physical bubbles, providing the correct choice per problem is sufficient.

So final answers per problem:

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Final Answer:
1. B
2. F
3. G
4. J
5. M
6. P
7. U