Solve the simultaneous equations: y = 3 x^(2) and 5x + y = 2

Question

Solve the simultaneous equations: y =
`3 x^(2)` and
`5x + y = 2`

Answer 1

I hope this helps you

Answer 2

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