Question

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

Answer 1

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)}

Answer 2

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