Question

[6.03] What is the value of the x variable in the solution to the following system of equations?

3x + 2y = 8
2x + 3y = 2

4

−2

x can be any number as there are infinitely many solutions to this system

There is no x value as there is no solution to this system

Answer 1

Solve for y for one equation and plug it into the second. First equation can be made into y = 4 - 3/2x. Put that in the second equation which would make it 2x + 3(4 - 3/2x) = 2 which makes it 2x + 12 - 9/2x = 2. Minus the 12 from each side and add the x terms up to get -5/2x = -10. To get x alone, multiply each side by the coeficient's reciprical which is -2/5 to get x = 20/5 which reduces down to x = 4.