Question

PLEASE GIVE ANSWER!

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


A )

B )

C )

D )

Answer 1

(1, 1 )

Explanation:

y = 3x - 2 → (1)

y = - 2x + 3 → (2)

substitute y = 3x - 2 into (2)

3x - 2 = - 2x + 3 ( add 2x to both sides )

5x - 2 = 3 ( add 2 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

substitute x = 1 into either of the 2 equations

substituting into (1)

y = 3(1) - 2 = 3 - 2 = 1

solution is (1, 1 )

Answer 2

(1,1)

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)