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.

- help_people

- jamiebookeater

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- help_people

@midhun.madhu1987

- welshfella

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

- midhun.madhu1987

General form of a linear equation is:
ax + by + c = 0
General form of a Quadratic equation is:
a(x^2) + bx + c = 0

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## More answers

- help_people

ok basically like @welshfella said

- help_people

how would i solve algebraically though?

- midhun.madhu1987

Equate both equtions:
2x + 1 = x^2 - x - 6
Now arrange it...by combining like terms...

- help_people

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

- help_people

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

- midhun.madhu1987

x^2 - x- 2x - 6-1 = 0
x^2 - 3x - 7 = 0

- midhun.madhu1987

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

- help_people

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

- midhun.madhu1987

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)

- midhun.madhu1987

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

- midhun.madhu1987

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)

- help_people

oh so that's part 1?

- midhun.madhu1987

Yes...

- help_people

that makes sense srry i was a little confused

- help_people

what would i do after>

- midhun.madhu1987

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

- help_people

ok :) ty!

- help_people

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

- welshfella

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

- help_people

oh so thats what i should use ?

- welshfella

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.

- welshfella

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

- help_people

yes he will i always use it :)

- welshfella

oh ok

- help_people

yep could you help with another one ?

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