Question

Nsider the following system of equations y=6x^2+1, y=x^2+4

Answer 1

The given equations are y= 6x^2+1 and y=x^2+4

Both the equations equal y so we can make them equal

6x^2+1=x^2+4

To bring x term on one side we subtract x^2 both sides

6x^2-x^2+1=4

5x^2+1=4

To isolate x term we subtract 1 both sides

5x^2=4-1

5x^2=3

Dividing by 5 both sides

X^2=3/5

Taking root of both sides we have:

X=±√⅗

Substituting x value to find y

When x=+√⅗=0.7745

Y= 6x^2+1

Y=6(3/5)+1

Y= 18/5+1

Y=23/5 =4.6

When x= -√⅗=-0.7745

Y= 6(3/5)+1

Y=23/5=4.6

Point of intersections are ( 0.7745,4.6) and (-0.7745,4.6)