Answer:
x= negative 1 and 2/5 y=1 and 3/5
Step-by-step explanation:
1. Start by putting both equations into slope-intercept form. (y=mx+b)
-3x+3y=9
-3x+3x+3y=9+3x
3y=9+3x
3y/3=9+3x/3
y=3+x
2x-7y=-14
2x-2x-7y=-14-2x
-7y=-14-2x
-7y/-7=-14/-7-2x/-7
y=2+2/7x
2. Graph the equations and find where they intercept.
Answer:
0.25k + 1.5 - k - 3.5 = -0.75k - 2.
Step-by-step explanation:
So, this question is basically asking us "If we had an x instead of a 2, would this be true?" We can try and see what we get:
![\frac{x^3+x^2+x}{x^2+x+1}=x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%5E3%2Bx%5E2%2Bx%7D%7Bx%5E2%2Bx%2B1%7D%3Dx%20)
So, if we want to show this we have to change the numerator or denominator in such a way that we can cancel some common factors. Notice that ![x^3+x^2+x=x(x^2+x+1)](https://tex.z-dn.net/?f=%20x%5E3%2Bx%5E2%2Bx%3Dx%28x%5E2%2Bx%2B1%29%20)
If we replace the factored numerator with the original one, we get:
![\frac{x(x^2+x+1)}{x^2+x+1}=x \implies \\ x=x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%28x%5E2%2Bx%2B1%29%7D%7Bx%5E2%2Bx%2B1%7D%3Dx%20%5Cimplies%20%5C%5C%20x%3Dx%20)
Since we have an equality, this relation is proved.
Let's calculate the slope of the A(3,1.5) and B(5, 2.5)
The formula of the slope m =(y₂-y₁)/(x₂-x₁)
m = (2.5 - 1.5)/(5 - 3)
m = (1)/(2) = 0.5
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