Write as a Vector Equality y=x^2+12x+30 , 8x-y=10

Problem

{[y=x2+12*x+30],[8*x−y=10])

Solution

1. Rearrange the second equation to solve for y so that both equations are in the same form.

8*x−y=10

−y=−8*x+10

y=8*x−10

2. Equate the two expressions for y to find the values of x where the curves intersect.

x2+12*x+30=8*x−10

3. Standardize the quadratic equation by moving all terms to one side to set the equation to zero.

x2+12*x−8*x+30+10=0

x2+4*x+40=0

4. Express the system as a single vector equation where the vector of functions equals the zero vector.

[[x2+12*x+30−y],[8*x−y−10]]=[[0],[0]]

Final Answer

[[y],[y]]=[[x2+12*x+30],[8*x−10]]

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