Answer:
[tex] \displaystyle ( x_{1},y_{1}) = (0.82, - 3.18) \\ ( x_{2},y_{2}) = ( - 0.82, - 4.82)[/tex]
Step-by-step 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:
[tex] \displaystyle {3x}^{2} + x - 6 = x - 4[/tex]
move right hand side expression to left hand side and change its sign so there's only 0 left on the left hand side:
[tex] \displaystyle {3x}^{2} + x - 6 - x + 4= 0[/tex]
simplify addition:
[tex] \displaystyle {3x}^{2} -2=0[/tex]
add 2 to both sides:
[tex] \displaystyle {3x}^{2} = 2[/tex]
divide both sides by 3
[tex] \displaystyle \frac{ {3x}^{2} }{3} = \frac{2}{3} [/tex]
[tex] \displaystyle {x}^{2} = \frac{2}{3} [/tex]
square root both sides:
[tex] \displaystyle {x} = \sqrt{\frac{2}{3} } \\ x = \frac{ \sqrt{2} }{ \sqrt{3} } [/tex]
rationalise the denominator by multiplying √3/√3:
[tex] \displaystyle x = \pm\frac{ \sqrt{6} }{3} = \pm0.82[/tex]
now let's figure out y
substitute the value of x to the linear equation:
[tex]y = \pm0.82 - 4[/tex]
when positive
[tex]y = - 3.18[/tex]
when negative
[tex]y = - 4.82[/tex]
Answer:
(x1,y1) = (0.82, - 3.18)
(x2,y2) = (-0.82, -4.82)
Step-by-step explanation:
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