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DSAT Math-Systems of two linear equations in two variables- Practice Questions

DSAT Math-Systems of two linear equations in two variables- Practice Questions

DSAT MAth Practice questions – all topics

  • Algebra Weightage: 35%  Questions: 13-15
    • Linear equations in one variable
    • Linear equations in two variables
    • Linear functions
    • Systems of two linear equations in two variables
    • Linear inequalities in one or two variables

DSAT MAth and English  – full syllabus practice tests

Question Easy

The graph of a system of linear equations is shown. What is the solution (x,y) to the system?

A) (0,3)
B) (1,3)
C) (2,3)
D) (3,3)

▶️ Answer/Explanation
Solution
1. Identify the intersection point of the two lines on the graph.
2. The solution occurs at the coordinates where both lines meet.
✅ Answer: C) (2,3)
Question Easy

Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for \$86, and Sofia purchased 3 shirts and 5 pairs of pants for \$166. Which of the following systems of linear equations represents the situation, if \(x\) represents the price, in dollars, of each shirt and \(y\) represents the price, in dollars, of each pair of pants?

A) \(4x + 2y = 86\)
\(3x + 5y = 166\)

B) \(4x + 3y = 86\)
\(2x + 5y = 166\)

C) \(4x + 2y = 166\)
\(3x + 5y = 86\)

D) \(4x + 3y = 166\)
\(2x + 5y = 86\)

▶️ Answer/Explanation
Solution
Rationale:
  • Hiro’s purchase: \(4\) shirts (\(x\) dollars each) and \(2\) pants (\(y\) dollars each) total \$86. This gives the equation \(4x + 2y = 86\).
  • Sofia’s purchase: \(3\) shirts (\(x\) dollars each) and \(5\) pants (\(y\) dollars each) total \$166. This gives the equation \(3x + 5y = 166\).
Why other options are incorrect:
  • B) Incorrectly swaps coefficients (number of shirts/pants).
  • C) Incorrectly swaps the total amounts spent.
  • D) Incorrectly swaps both coefficients and total amounts.
✅ Answer: A) \(4x + 2y = 86\), \(3x + 5y = 166\)
Question Easy

A petting zoo sells two types of tickets. The standard ticket, for admission only, costs \$5. The premium ticket, which includes admission and food to give to the animals, costs \$12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of \$2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, \(s\), and premium tickets, \(p\), sold on that Saturday?

A) \(s + p = 250\)
\(5s + 12p = 2,\!300\)

B) \(s + p = 250\)
\(12s + 5p = 2,\!300\)

C) \(5s + 12p = 250\)
\(s + p = 2,\!300\)

D) \(12s + 5p = 250\)
\(s + p = 2,\!300\)

▶️ Answer/Explanation
Solution
Rationale:
  • Total tickets sold: \(s + p = 250\) (standard plus premium tickets)
  • Total revenue: \(5s + 12p = 2,\!300\) (\$5 per standard ticket and \$12 per premium ticket)
Why other options are incorrect:
  • B) Incorrectly swaps the prices of standard and premium tickets
  • C) Incorrectly swaps the total tickets with total revenue amounts
  • D) Incorrectly swaps both prices and total amounts
✅ Answer: A) \(s + p = 250\), \(5s + 12p = 2,\!300\)

  Question Easy

y=18x+25
y =- 14x-7
What is the solution (x,y) to the given system of equations?

A. (-7,25)

B. (-1,7)

C. (7,-1)

D. (25,-7)

▶️ Answer/Explanation
Solution

To solve the system, set the equations equal to each other since they both equal \(y\):

\[ 18x + 25 = -14x – 7 \]

Solving for \(x\):

\[ \begin{aligned} 18x + 14x &= -7 – 25 \\ 32x &= -32 \\ x &= -1 \end{aligned} \]

Substitute \(x = -1\) into the first equation to find \(y\):

\[ \begin{aligned} y &= 18(-1) + 25 \\ y &= -18 + 25 \\ y &= 7 \end{aligned} \]

The solution \((x, y)\) to the system is \((-1, 7)\).

✅ Answer: B) \((-1, 7)\)
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