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)

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

(x+3)(x+7)

step-by-step explanation: