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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

2 Answers

4 votes

Answer: Third Option

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

Explanation:

We have the following system of equations:


y = x^2 - x-3


y=-3x + 5

We have the first three steps to solve the system.


x^2- x-3 = -3x +5 equal both equations


0 = x^2 + 2x - 8 Simplify and equalize to zero


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

Then note that the equation is equal to zero when
x = 2 or
x = -4

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


y=-3(2) + 5


y=-6 + 5


y=-1

First solution: (2, -1)


y=-3(-4) + 5


y=12 + 5


y=17

Second solution: (-4, 17)

The answer is the third option

User MiffTheFox
by
9.4k points
1 vote

Answer:

Option C is correct.

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.

User Dan Torrey
by
7.5k points

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