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Math Assessment

Linear Equations in Two Variables - Mastery Challenge

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Linear Equations in Two Variables - Mastery Challenge

Linear Equations in Two Variables

Mastery Challenge (30 MCQ) | Level: Medium

Section A: Systems & Algebraic Methods
1. Solve for $x$ and $y$:
3x + 2y = 11
2x + 3y = 4
2. Solve using substitution:
x - y = 3
x/3 + y/2 = 6
3. For what value of $k$ will the system $3x + y = 1$ and $(2k-1)x + (k-1)y = 2k+1$ have no solution?
4. Solve: $0.4x + 0.3y = 1.7$ and $0.7x - 0.2y = 0.8$
5. If $2x + y = 23$ and $4x - y = 19$, find the value of $5y - 2x$.
6. Intersection point of $2x + 3y = 12$ and $x - y = 1$ is:
7. Find $k$ for infinite solutions: $2x + 3y = 7$ and $(k-1)x + (k+2)y = 3k$
8. Solutions for $2/x + 3/y = 13$ and $5/x - 4/y = -2$:
9. If $x-y=2$ and $x+y=4$, then $x$ and $y$ are:
10. Value of $x+y$ for $152x - 378y = -74$ and $-378x + 152y = -604$ is:
11. Value of $m$ in $y = mx + 3$ if $2x + 3y = 11$ and $2x - 4y = -24$:
12. Solution to $x/a + y/b = 2$ and $ax - by = a^2 - b^2$:
13. Area of triangle formed by $2x + 3y = 12$ and coordinate axes:
14. Solve $8x + 5y = 9$ and $3x + 2y = 4$ for $x$:
15. Condition for unique solution: $kx - y = 2$ and $6x - 2y = 3$
Section B: Word Problems & Applications
16. Sum of two numbers is 35, difference is 13. The numbers are:
17. A father's age is 3x the sum of ages of his two children. After 5 years, his age is 2x the sum. Father's age:
18. A fraction becomes 9/11 if 2 added to both N/D; 5/6 if 3 added to both. The fraction is:
19. Taxi: 10km for $105, 15km for $155. Fixed charge and rate per km:
20. 5 pencils + 7 pens = $50; 7 pencils + 5 pens = $46. Cost of one pen:
21. Boat speed in still water is 8km/h, stream is 3km/h. Speed downstream:
22. Sum of digits of 2-digit number is 9. 9x Number = 2x Reverse. Number is:
23. 100km apart. Meet in 5h (same dir), 1h (opposite dir). Speeds:
24. Score 40 (3 for right, -1 for wrong); Score 50 (4 for right, -2 for wrong). Total questions:
25. Perimeter is 36m. Length is 4m more than width. Length is:
26. 2W + 5M = 4 days; 3W + 6M = 3 days. Time for 1 Woman alone:
27. For $2/x + 3/y = 13$ and $5/x - 4/y = -2$, find $x$:
28. $a, b$ for infinite solutions of $2x + 3y = 7$ and $(a-b)x + (a+b)y = 3a+b-2$:
29. Hostel: 20 days = $1000; 26 days = $1180. Fixed charge is:
30. In $\Delta ABC$, $\angle C = 3\angle B = 2(\angle A + \angle B)$. Angle $C$ is:
© 2024 Math Olympiad Preparation - Linear Equations MCQ Series
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