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

If on dividing 26 into two parts, we find that three times the first and seven times the second part together equals to 122. Then, the ratio of first and second part shall be:

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:

The system of linear equations 3x + y + 4 = 0 and 2x + y + 9 = 0 has:

The pair of equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 represents two lines, which are ?

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

A. x + y – 5 = 0, 3x + 2y – 10 = 0

B. 3x – 2y – 6 = 0, 6x – 4y – 12 = 0

C. x – y – 9 = 0, 3x – 3y – 27 = 0

D. x + y – 4 = 0 , 3x + 3y – 12 = 0

Choose the correct option from the given below:

Which of the following pair of linear equations has / have many infinite solutions?

A. $9x + 3y + 12 = 0$; and $18x + 6y + 24 = 0$

B. $2x - 3y = 13$; and $7x - 2y = 20$

C. $x + y = 5$; and $2x + 2y = 10$

D. $3x + y - 3 = 0$; and $2x + \dfrac{2}{3}y = 2$

Choose the correct answer from the options given below: