What are the solutions of this system of equations?
the first three steps in determining the solution set of the
system of equations algebraically are shown.
y = x2 - x-3
y=-3x + 5
(-2, -1) and (4, 17)
(-2, 11) and (4, -7)
(2, -1) and (-4, 17)
(2, 11) and (-4,-7)
step
1
2
equation
x– x-3 = -3x +5
0 = x² + 2x - 8
0 = (x-2)(x+4)
3

Option C is correct.

Step-by-step explanation:

y = x^2-x-3     eq(1)

y = -3x + 5      eq(2)

We can solve by substituting the value of y in eq(2) in the eq(1)

-3x+5 = x^2-x-3

x^2-x+3x-3-5=0

x^2+2x-8=0

Now factorizing the above equation

x^2+4x-2x-8=0

x(x+4)-2(x+4)=0

(x-2)(x+4)=0

(x-2)=0 and (x+4)=0

x=2 and x=-4

Now finding the value of y by placing value of x in the above eq(2)

put x =2

y = -3x + 5

y = -3(2) + 5

y = -6+5

y = -1

Now, put x = -4

y = -3x + 5

y = -3(-4) + 5

y = 12+5

y =17

so, when x=2, y =-1 and x=-4 y=17

(2,-1) and (-4,17) is the solution.

So, Option C is correct.

Third Option

(2, -1) and (-4, 17)

Step-by-step explanation:

We have the following system of equations:

We have the first three steps to solve the system.

  equal both equations

     Simplify and equalize to zero

    Factorize

Then note that the equation is equal to zero when or

Now substitute the values of x in either of the two situations to obtain the value of the variable y.

First solution: (2, -1)

Second solution: (-4, 17)

The answer is the third option

2

step-by-step explanation: