Question

Create a system of equations that includes one linear equation and one quadratic equation.

Part 1. Show all work to solving your system of equations algebraically.

Part 2. Graph your system of equations, and show the solution graphically to verify your solution.

Answer 1

@midhun.madhu1987

Answer 2

try using

y = 2x + 1
y = x^2 - x - 6

Answer 3

General form of a linear equation is:

ax + by + c = 0

General form of a Quadratic equation is:

a(x^2) + bx + c = 0

Answer 4

ok basically like @welshfella said

Answer 5

how would i solve algebraically though?

Answer 6

Equate both equtions:

2x + 1 = x^2 - x - 6

Now arrange it...by combining like terms...

Answer 7

I'm not sure/// comine 2x-x?

Answer 8

how can you combine you put the stuff on the other side of the equal sign

Answer 9

x^2 - x- 2x - 6-1 = 0

x^2 - 3x - 7 = 0

Answer 10

Now you can solve this quadratic equation using QUadratic Formula...

Answer 11

wait can you tell me what we have doen so far and wha i should put ?

Answer 12

Solve this system of equations algebraically:

y = x2 - x - 6 (quadratic equation in one variable of form y = ax2 + bx + c )
y = 2x - 2 (linear equation of form y = mx + b)

Answer 13

Substitute from the linear equation into the quadratic equation and solve.
y = x2 - x - 6
2x - 2 = x2 - x - 6
2x = x2 - x - 4

0 = x2 - 3x - 4

0 =(x - 4)(x + 1)

x - 4 = 0 OR x + 1 =0
x = 4 x = -1

Answer 14

Find the y-values by substituting each value of x into the linear
equation.

y = 2(4) - 2 = 6
POINT (4,6)

y = 2(-1) - 2 = -4
POINT (-1,-4)

Answer 15

oh so that's part 1?

Answer 16

Yes...

Answer 17

that makes sense srry i was a little confused

Answer 18

what would i do after>

Answer 19

Now you can plot the points graphically and check...

Answer 20

ok :) ty!

Answer 21

wait @midhun.madhu1987 what do they mean how the solution graphically ?

Answer 22

https://www.desmos.com/screenshot/rljjhtzr7b

to graph you plot points for a range of x and y

the above link shows the graphs
where they intersect are the solutions

Answer 23

oh so thats what i should use ?

Answer 24

as you see they intersect at (4,6) and (-1,-4) which agrees with the values you got earlier.
I'm not sure Desmos Graphing is a very good piece of software but i dont know if your teacher will allow it.

Answer 25

He/she might only accept a drawing on graph paper.

Answer 26

yes he will i always use it :)

Answer 27

oh ok

Answer 28

yep could you help with another one ?