Explain how you can determine that the following system has one unique solution – without actually solving the system. 2x+y=4 , 2y=6-2x

Both equations has different slope , so the system of equation have one unique solution.

Step-by-step explanation:

,

To determine that the system of equation has unique solution, we need to find out the slope.

To find slope, we write the equation in the form of y=mx+b

Where m  is the slope and b is the y intercept

Subtract 2x on both sides

here, m= -2 is the slope

Divide both sides by 2

Slope m = -1

Both equations has different slope , so the system of equation have one unique solution.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3