Linear equations 3x + 5y = 19 and 10x - 3y = 24 have solution x = ()/3 and y = ()/2, then the value of + is: Option 1: 5 Option 2: 13 Option 3: 10 Option 4: 7

Answer: 13. Solution: Substituting x = ()/3, y = ()/2: from the first equation, 2 + 5 = 38; from the second, 20 - 9 = 144. Solving simultaneously gives = 9, = 4. So + = 13.

Quantitative Reasoning

Linear Equation

Medium

Linear equations $3x + 5y = 19$ and $10x - 3y = 24$ have solution $x = \frac{\alpha}{3}$ and $y = \frac{\beta}{2}$ , then the value of $\alpha + \beta$ is:

✅ Correct Option: 2

Substituting $x = \frac{\alpha}{3}$ , $y = \frac{\beta}{2}$ : from the first equation, $2\alpha + 5\beta = 38$ ; from the second, $20\alpha - 9\beta = 144$ . Solving simultaneously gives $\alpha = 9$ , $\beta = 4$ .

So $\alpha + \beta = 13$ .

2026: 14 May Shift 2

Solve the linear equation for $x$ :

$3x - 7 = 2x + 5$

2025: 19 May Shift 1

If 2x + 3y = 26 and y - x = 2, then the value of x + y is:

2025: 26 May Shift 1

Seven chairs and three tables together cost ₹ 7400, three chairs and five tables together cost ₹ 5400. The total cost (in ₹) of 1 chair and 2 tables is:

2025: 21 May Shift 1

If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$ , then what is the value of x?

2026: 18 May Shift 2

Which of the following pairs of linear equations is/are consistent?

A. $x + y = 5, 2x + 2y = 10$

B. $2x + y - 6 = 0, 4x - 2y - 4 = 0$

C. $x - y = 8, 3x - 3y = 16$

D. $x - 2y = 0, 3x + 4y - 20 = 0$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

For what value of k, the system of equations $kx + 4y - k + 4 = 0$ and $16x + ky = k$ has an infinite number of solutions?

Linear equations 3x+5y=193x + 5y = 193x+5y=19 and 10x−3y=2410x - 3y = 2410x−3y=24 have solution x=α3x = \frac{\alpha}{3}x=3α​ and y=β2y = \frac{\beta}{2}y=2β​, then the value of α+β\alpha + \betaα+β is:

Solution

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CUET General Test Past Year Questions (Topic-Wise)

Linear equations $3x + 5y = 19$ and $10x - 3y = 24$ have solution $x = \frac{\alpha}{3}$ and $y = \frac{\beta}{2}$ , then the value of $\alpha + \beta$ is: