Question

For which values of a the system has at least one solution:
`x \leqslant 7 \\ x \geqslant a`URGENT PLS HELP

Answer 1

You have the following system of equations:

x ≤ 7

x ≥ a

In order to determine the value of a for the system has at least one solution you take into account that the first inequality stablishes that x values can be from - infinty to 7. The second inequality stablishes that x values can be all numbers lower or equal of a certan value a. The solution of the system are the values of x available for both inequalities. Or in other words, the solution of the system is the intersection of both interval.

Then, whichever value of a lower than 7 allows that the system of equations has a valid solution. If you need only one available value, then a = 7 because the inequalities also include the limits of the interval.

Then, a must be, at least 7, a = 7