Question

solve the system of equations
3x+6y=21
-5x+2y=13

Answer 1

To solve the system of equations:

1) Multiply the first equation by 2 and the second equation by 3 to eliminate the x term:
2(3x + 6y) = 2(21), simplifies to: 6x + 12y = 42
3(-5x + 2y) = 3(13), simplifies to: -15x + 6y = 39

2) Adding the two new equations together will eliminate the y term:
(6x + 12y) + (-15x + 6y) = 42 + 39
Combine like terms: -9x + 18y = 81

3) Divide the entire equation by 9 to simplify:
(-9x + 18y)/9 = 81/9
Simplifies to: -x + 2y = 9

So the new system of equations is:
-9x + 18y = 81
-x + 2y = 9

4) Multiply the second equation by 9:
9(-x + 2y) = 9(9)
Simplifies to: -9x + 18y = 81

Comparing this result to the first equation, you can see that they are the same equation. Therefore, this system of equations is dependent and has infinitely many solutions.