y=3x²
5x+y=2
We can solve this system of equations by substitution method.
5x+(3x²)=2
3x²+5x-2=0
Now, we solve this square equation.
x=[-5⁺₋√(25+24)]/6=(-5⁺₋7)/6
We have two solution:
x₁=(-5-7)/6=-2 ⇒y₁=3x²=3(-2)²=12
x₂=(-5+7)/6=1/3 ⇒y₂=3(1/3)²=2/9=1/3
Answer: We have two solutions:
Solution₁; x₁=-2, y₁=12
Solution₂: x₂=1/3, y₂=1/3
