1. ## Stuck!!

(a) Give the value of for which the system of equations

has an infinite number of solutions.

(b) With as in your answer to part (a), find a particular solution to this system.

2. Originally Posted by mr_motivator
(a) Give the value of for which the system of equations

has an infinite number of solutions.

(b) With as in your answer to part (a), find a particular solution to this system.
The first equation can be written 4x - 10y = 6. Compare this with the second ....

3. ## Simultaneous equations

Hello mr_motivator
Originally Posted by mr_motivator
(a) Give the value of for which the system of equations

has an infinite number of solutions.

(b) With as in your answer to part (a), find a particular solution to this system.
If, when you're solving simultaneous equations, there's an infinite number of solutions, then the equations are not independent. In the case of 2 equations in 2 unknowns, this simply means that one equation is a multiple of the other. So here, $\displaystyle b = 4$, and both sides of the second equation are clearly twice the first.

When $\displaystyle b = 4$, any value of $\displaystyle x$ will do to find a corresponding value of $\displaystyle y$.

E.g. $\displaystyle x = 1, y = -\frac{1}{5}$