Math please help me ;)?

Question

Suppose we want to find where the lines y=3x+15 and y=3-3x cross and we want to be more accurate than the graph paper will let us be.

a)Find the point of intersection using algebra .

b)Since y=3x+15 and y=3-3x what must be tru about 3x+15 and 3-3x?

c)Write an equation which contains no y's and solve it for x.

d)Use the x-value you found in part (c) to find the corresponding y-value.

e)Where do the two lines cross?

Answer 1

Parts (b) to (e) are guiding you to the answer for (a).

(b)

As y is equal to both 3x + 15 and 3 - 3x, these two expressions in x are equal to each other.

(c)

Equating the two values:

3x + 15 = 3 - 3x

Adding 3x to each side:

6x + 15 = 3

Subtracting 15 from each side;

6x = - 12

Dividing by 6:

x = - 2.

(d)

As y = 3x + 15,

y = 3(- 2) + 15

= - 6 + 15

= 9.

The other equation should give the same result:

y = 3 - 3x

= 3 - 3(- 2)

= 3 + 6

= 9.

(e)

The lines cross at (- 2, 9).

That is also the answer to (a).