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Algebra 1: Solving Linear Equations and Systems

Solve for x, work with slope and lines, solve systems of equations, inequalities and absolute value equations, plus a few word problems. Every answer shows the steps.

by Kill h.18 questionsCreated Nov 8, 2026, 08:04 PM

Algebra· Linear Equations#algebra#linear-equations#solve-for-x#systems-of-equations

18 questions

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1
Solve for x:
- A
- B
- C
Subtract 7 from both sides: . Divide by 3: . Check: . comes from adding 7 instead of subtracting.
2
Solve for x:
- B
- C
- D
Distribute: . Subtract 3x: . Add 10: , so . Getting means the 5 was not distributed to the 2 ().
3
Solve for x:
- A
- B
- C
Add 3: . Multiply both sides by 4: . Dividing 5 by 4 (giving 1.25) undoes the operation the wrong way.
4
Solve for x:
- A
- C
- D
Distribute: . Combine like terms: , so and . 4.5 comes from writing instead of .
5
Solve for x:
- A
- B
- D
Multiply every term by the LCD, 6: . Subtract 3x and 6: . Clearing fractions first avoids most mistakes; just remember to multiply the constants too.
6
What is the slope of the line through (2, 3) and (6, 11)?
- B
- C
- D
. puts run over rise. 8 is only the change in y.
7
Which equation describes the line with slope −3 that passes through (1, 4)?
- A
- C
- D
Point-slope form: , so . Check: at x = 1, y = 4. Using 4 as the intercept forgets that (1, 4) is not on the y-axis.
8
What is the slope of a line perpendicular to ?
- B
- C
- D
Perpendicular slopes are negative reciprocals, so their product is −1: . A parallel line would have the same slope, 2.
9
Where does cross the x-axis?
- (4, 0)
- B
  (0, −3)
- C
  (−3, 0)
- D
  (0, 4)
On the x-axis, y = 0: , so x = 4, giving (4, 0). (0, −3) is the y-intercept, found by setting x = 0.
10
Solve the system: and
- A
- B
- D
Add the equations (elimination): , so x = 7. Then , so y = 3. Check the second equation: 7 − 3 = 4. Swapping x and y fails that check.
11
Solve the system: and
- A
- B
- D
Substitute: , so , and y = 2. Then . Check: .
12
How many solutions does this system have: and ?
- No solution
- B
  Exactly one
- C
  Exactly two
- D
  Infinitely many
Doubling the first equation gives , which contradicts . The lines have the same slope (−2) but different intercepts, so they are parallel and never meet. Infinitely many would need identical lines.
13
Solve the inequality:
- A
- B
- D
Subtract 5: . Divide by −2 and flip the inequality sign: . Forgetting the flip when dividing by a negative gives . Check with x = −4: .
14
Solve:
- or
- B
  only
- C
  or
- D
  only
The expression inside can be 7 or −7: gives x = 10, and gives x = −4. Both are 7 units from 3 on the number line.
15
Solve for h.
- A
- B
- D
Multiply both sides by 2: . Divide by b: . Check with b = 4, h = 3: A = 6, and .
16
A phone plan costs $20 per month plus $0.10 per text. One month's bill is $35. How many texts were sent?
- A
  350
- B
  15
- C
  550
- 150
Write . Subtract 20: , so . 350 comes from adding the $20 instead of subtracting it.
17
The sum of three consecutive integers is 51. What is the smallest of them?
- A
  17
- B
  15
- 16
- D
  18
Let them be n, n + 1, n + 2. Then , so and n = 16. The integers are 16, 17, 18. 17 is the middle one (51 ÷ 3).
18
Solve for x:
- A
- B
- C
Subtract 0.3x: . Add 1.2: , so x = 10. Tip: multiply everything by 10 first to get . 2.5 comes from adding the x terms (0.8x = 2).