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.
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y = 2x + 1
y = x^2 - x - 6
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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ok basically like @welshfella said
how would i solve algebraically though?
Equate both equtions:
2x + 1 = x^2 - x - 6
Now arrange it...by combining like terms...
I'm not sure/// comine 2x-x?
how can you combine you put the stuff on the other side of the equal sign
x^2 - x- 2x - 6-1 = 0
x^2 - 3x - 7 = 0
Now you can solve this quadratic equation using QUadratic Formula...
wait can you tell me what we have doen so far and wha i should put ?
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)
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
Find the y-values by substituting each value of x into the linear
y = 2(4) - 2 = 6
y = 2(-1) - 2 = -4
oh so that's part 1?
that makes sense srry i was a little confused
what would i do after>
Now you can plot the points graphically and check...
ok :) ty!
wait @midhun.madhu1987 what do they mean how the solution graphically ?
to graph you plot points for a range of x and y
the above link shows the graphs
where they intersect are the solutions
oh so thats what i should use ?
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.
He/she might only accept a drawing on graph paper.