Which of the following statement is true for the equation 2x + 3y = 15

Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = −2 .

The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is  _______.  

A pair of linear equations has no solution then the graphical representation is _______.

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { { c }_{ 1 } }{ { c }_{ 2 } } \) where a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 then the given pair of linear equation has _________ solution(s)

Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.

A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmadabad costs Rs. 216 and one full and one half reserved first class ticket costs Rs. 327. What is the basic first class full fare and what is the reservation charge?

(Computing slope made easier!) Find the slope and y-intercept of the line given by the equation 2y – 3x = 12.

Solve the system of linear equations x + 3y = 16 and 2x − y = 4 by substitution method.

Find the value of k for which the system of linear equations 8x + 5y = 9; kx +10y = 15 has no solution.

The sum of the digits of a given two digit number is 5. If the digits are reversed, the new number is reduced by 27. Find the given number.

Check whether the following system of equation is consistent or inconsistent and say how many solutions we can have if it is consistent.
(i) 2x – 4y = 7
x – 3y = –2
(ii) 4x + y = 3
8x + 2y = 6
(iii) 4x +7 = 2 y
2x + 9 = y