Question

i need help plz
Solve this non-linear system of equations. Explain your work and show all steps, neatly (please note that the symbol ^ refers to an exponent. The first equation is read as “y equals x squared plus 3x minus 7).
Y = x^2 + 3x - 7
3x - y = -2

Answer 1

ok... so take the 2nd equation and make y the subject, what do you get...?

Answer 2

idk

Answer 3

ok... so its a case of adding y to both sides of the equation

3x = y + 2

now subtract 2 from both sides of the equation, what do you get..?

Answer 4

1x = y?

Answer 5

nope... oops and my mistake, it should have been add 2 to both sides of the equation

3x + 2 = y

so now both equations are in the form y = .....

so you can equate them

x^2 + 3x - 7 = 3x + 2

so you have a quadratic equation equal to a linear equation, this means there are possibly 2 points of intersection..

so you now need to solve

\[x^2 + 3x - 7 = 3x + 2\]

start by addint 7 to both sides of the equation.

Answer 6

x^2 + 3x = 3x + 9?

Answer 7

great now subtract 3x from both sides of the equation

Answer 8

x^2 = x +9?

Answer 9

not quite

x^2 + 3x = 3x + 9
- 3x -3x
---------------------
x^2 = 9

there are 2 values for x, what are they... take the square root of both sides..

Answer 10

x^2 = 3

Answer 11

not quite \[\sqrt{x^2} = \pm x\]

so then using this idea

\[x = \pm 3\]

or

x = 3 and x = -3

to find the ordered pairs substitute each x value into the equation

y = 3x + 2 to find the corresponding y values

hope it makes sense

Answer 12

it does