how do you solve {5bx-6a=-3b-4ax and 5x-1=-3b-4ax using system of equations?

Question

I have no idea how to solve this so if anyone could possibly show me would be greatly appreciated!

Answer 1

You have 3 variables (a, b, x) but only 1 equation.  Normally it takes the same number of equations as variables to solve.  A bit of quick checking. . .

.

5bx - 6a = -3b - 4ax

5bx + 4ax = 6a - 3b

(5b + 4a)x = 6a - 3b

x = (6a - 3b) / (5b + 4a)

.

5x - 1 = -3b - 4ax

5x + 4ax = 1 - 3b

(5 + 4a)x = 1 - 3b

x = (1 - 3b) / (5 + 4a)

.

(6a - 3b) / (5b + 4a) = (1 - 3b) / (5 + 4a)

(6a - 3b) (5 + 4a) = (1 - 3b) (5b + 4a)

30a + 24a^2 - 15b - 12ab = 5b + 4a - 15b^2 - 12ab

30a + 24a^2 - 15b = 5b + 4a - 15b^2

24a^2 + 26a - 20b + 15b^2 = 0

.

With one equation we can eliminate 1 variable, but since we started with 3 variables, we're still left with 2 variables.