Solve for x and y simultaneously x-2y=3. 3x²-5xy-16y=24

Hello,

x=3+2y

==> 3 (3+2y) ²-5 (3+2y) y-16y=24

==>2y²+5y+3=0

==> (y=-3/2 and x = 0 or y=-1 and x=1)

sol={ (0,-3/2), (1,-1) }

X-2y=3 ⇒y = (x-3) / 2

3x²-5xy-16y=24

We can suggest this system of equations by substitution method.

y = (x-3) / 2

3x²-5x (x-3) / 2-16 (x-3) / 2=24

least common multiple=2

6x²-5x (x-3) - 16 (x-3) = 48

6x²-5x²+15x-16x+48=48

x²-x=0

x (x-1) = 0

Now, we solve two equations:

1) x=0 ⇒y = (0-3) / 2=-3/2

2) x-1=0

x=1 ⇒y = (1-3) / 2=-1

Answer: we can two solutions:

solution1: x=0; y=-3/2

solution2: x=1, y=-1