Worksheet · solutions includedLinear Equations & Systems — Practice Worksheet
Try each problem first, then click Show solution. To print an answer key, open all solutions before File ▸ Print.
Section A — the questions you missed
Original — Math M1 Q9 (you answered 1)
If 4x − 4 = 112, what is the positive value of x − 1?
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4x = 116 → x = 29.
The question asks for x − 1 = 28 (not x). Read the ask!
Answer: 28
Original — Math M1 Q22 (you answered 5)
The graph of 9x − 10y = 19 is translated down 4 units. What is the x-coordinate of the x-intercept of the resulting graph?
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y → y + 4: 9x − 10(y + 4) = 19 → 9x − 10y = 59.
Set y = 0: x = 59/9 ≈ 6.556.
Answer: 59/9 (≈ 6.556)
Original — Math M2 Q11 (you answered 2)
In 2kx − n = (−28/15)x − (36/19), k and n are constants with n > 1. The equation has no solution. What is k?
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No solution → the x-coefficients must match while constants differ.
2k = −28/15 → k = −14/15.
Answer: −14/15 (≈ −0.933)
Original — Math M2 Q4 (you answered B; correct C)
A line passes through (0, 7) and (8, 0). The point (d, 4) lies on the line. What is d? (Answer choices are fractions: 7/2, 26/7, 24/7, 27/8.)
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Slope = (0 − 7)/(8 − 0) = −7/8, so y = 7 − (7/8)x.
Set y = 4: 4 = 7 − (7/8)d → (7/8)d = 3 → d = 24/7.
Answer: C) 24/7
Section B — new practice (same skills)
Practice 1
For what value of a does the system y = 3x + 1 and y = ax − 4 have no solution?
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No solution → equal slopes, different intercepts.
a = 3 (intercepts 1 ≠ −4, so parallel). a = 3.
Answer: 3
Practice 2
The line 2x + 5y = 20 is translated down 3 units. Find the new x-intercept.
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y → y + 3: 2x + 5(y + 3) = 20 → 2x + 5y = 5.
y = 0 → x = 5/2 = 2.5.
Answer: 2.5
Practice 3
If 6x + 3 = 39, what is the value of 2x + 1?
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6x = 36 → x = 6. Then 2x + 1 = 13. (Read what’s asked.)
Answer: 13
Practice 4
A line passes through (0, −3) and (4, 5). Find the x-intercept.
Show solution
Slope = (5 − (−3))/(4 − 0) = 8/4 = 2, so y = 2x − 3.
y = 0 → x = 3/2 = 1.5.
Answer: 1.5