The first two steps in determining the solution set of the system of equations, y = x2 – 2x – 3 and y = –x +3, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 0) and (–2, 5) (–6, 9) and (1, 2) (–3, 6) and (2, 1) (6, –3) and (–1, 4)

y = x^2 - 2x - 3
y = -x + 3

-x + 3 = x^2 - 2x - 3
x^2 - 2x - 3 + x - 3 = 0
x^2 -x - 6 = 0
(x - 3)(x + 2) = 0

x - 3 = 0 y = -x + 3
x = 3 y = -3 + 3
y = 0

x + 2 = 0 y = -x + 3
x = -2 y = -(-2) + 3
y = 2 + 3
y = 5

solutions are : (3,0) and (-2,5)

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keshavgandhi04 keshavgandhi04 · Answer 2 · 2022-02-03T18:03:35+01:00

The first two steps in determining the solution set of the system of equations

[tex]\rm y = x^{2} -2x - 3\\ y = -x +3,[/tex]

How to solve the solution set of the system of equations?

To solve a system of equations by the help of graph , we will graph all the equations given in the system.

The point on which all the plotted lines intersect are called the solutions to the system.

Graph of System here the two lines intersect at the point example,(1, 1), this point will be called as solution to the system,This is the format of solving the a system of equations.

Here acccording to the given question,

To represents the solution of this system of equations we need to solve this accoding to the concept of simultaneous equation of system of equation.

[tex]\rm -x + 3 = x^2 - 2x - 3\\x^2 - 2x - 3 + x - 3 = 0\\x^2 -x - 6 = 0\\(x - 3)(x + 2) = 0[/tex]

Now, we will put the value in the equation

if x-3 = 0 , x = 3 in equation y = -x + 3 we get ,

y = -3 + 3

y = 0

Similarly,

if x+2 = 0 , x = -2 in equation y = -x + 3 we get ,

y = -(-2) + 3

y = 5

Therefore, The solution set of the system of equations,

[tex]\rm y = x^{2} -2x - 3\\ y = -x +3,[/tex] will be (3,0) and (-2,5)

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