LOT OF POINTS approximate the solutions to this system. y = 3x2 + x − 6 y = x − 4 Round your answers to the nearest hundredth.

Question

asked Aug 26, 2022 120k views

2 Answers

SiddharthaRT · Answer 1 · 2022-09-01T22:55:14+0000

Answer:

$\displaystyle ( x_(1),y_(1)) = (0.82, - 3.18) \\ ( x_(2),y_(2)) = ( - 0.82, - 4.82)$

Explanation:

we are given a system of quadratic and linear equation

we want to figure out x and y

in other words the coordinates where the linear function intercept quadrilateral function

to do so

you can use substitution method

since y equals to both equation so substitute:

$\displaystyle {3x}^(2) + x - 6 = x - 4$

move right hand side expression to left hand side and change its sign so there's only 0 left on the left hand side:

$\displaystyle {3x}^(2) + x - 6 - x + 4= 0$

simplify addition:

$\displaystyle {3x}^(2) -2=0$

add 2 to both sides:

$\displaystyle {3x}^(2) = 2$

divide both sides by 3

$\displaystyle \frac{ {3x}^(2) }{3} = (2)/(3)$

$\displaystyle {x}^(2) = (2)/(3)$

square root both sides:

$\displaystyle {x} = \sqrt{(2)/(3) } \\ x = ( √(2) )/( √(3) )$

rationalise the denominator by multiplying √3/√3:

$\displaystyle x = \pm( √(6) )/(3) = \pm0.82$

now let's figure out y

substitute the value of x to the linear equation:

$y = \pm0.82 - 4$

when positive

y = - 3.18

when negative

y = - 4.82