PLEASE GIVE ANSWER! Which point satisfies the system of equations y = 3x − 2 and y = -2x + 3?

A )

B )

C )

D )

(1,1)

Step-by-step explanation:

The question is asking if there is a point, (x,y), that satisfies (works) for both equations.  Is there a combination of x and y that works in both.

We can solve this in one of two ways:  mathematically and graphically.  If the lines intersect, then they will have the one common value of (x,y).

Mathematically:

y = 3x − 2  

y = -2x + 3

Set them equal to each other (i.e., y = y)

3x − 2 = -2x + 3

5x = 5

x = 1

Use this value of x in either equation to find y:

y = 3x − 2

y = 3(1) − 2

y = 1

The common point is (1,1)

Graphically:

Plot the two lines and look for the intersection point.  See attached.

See attachment.

They intersect at (1,1)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.