If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this.
m - 2n = 16,
4m + 4 = 1
....this question have trivial solution
m=-3/4
n=-67/8
what is 28%out of 11 in math
To determine the solution set of the system, let's first solve each equation separately.
Equation 1: m - 2n = 16
To solve for m, you can isolate m by adding 2n to both sides:
m = 16 + 2n
Equation 2: 4m + 4 = 1
To solve for m, you can isolate m by subtracting 4 from both sides and then dividing both sides by 4:
4m = 1 - 4
4m = -3
m = -3/4
Now that we have solved for m in both equations, we can express the solution set using set-builder notation.
Since the value of m in equation 1 is in terms of n (m = 16 + 2n), we can express the solution set for the system using set-builder notation as follows:
{(m, n) ∈ ℝ² | m = 16 + 2n}
This means that for any value of n, m will be equal to 16 plus twice the value of n. Therefore, the system has an infinite number of solutions.