Question

9. Find the point of intersection of the lines: y = 4x + 1 and y = - 2x + 4 A. (2,9) B.(1/2,3) C. (1,2) D. (1/4,2)

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Answer 1

Explanation:

y = 4x + 1

A.(2,9)

y = 4(2) + 1 = 9

y = 9.

y = 4x + 1

9 = 4x + 1

9 - 1 = 4x

8 = 4x => x = 8÷4 = 2

x = 2.

y = -2x + 4.

A.(2,9)

y = -2(2) + 4 = 0

y = 0.

y = - 2x + 4

0 = -2x + 4

0 - 4 = 2x

0 = 2x => x = 0 ÷ 2 = 0

x = 0.

y = 4x + 1

B.(1/2, 3)

y = 4(1/2) + 1

y = 4 ÷ 2 + 1 = 3

y = 3.

y = 4x + 1

3 = 4x + 1

3 - 1 = 4x

2 = 4x => x = 2 ÷ 4 = 1/2

x = 1/2.

y = - 2x + 4

B.(1/2, 3)

3 = - 2x + 4

3 - 4 = - 2x

- 1 = - 2x => x = 1/2

x = 1/2.

y = - 2x + 4

y = - 2(1/2) + 4

y = -2(0.5)+ 4

y = -1 + 4 = 3

y = 4x + 1

C.(1,2)

y = 4(1) + 1 = 5

y = 5.

y = 4x + 1

5 = 4x + 1

5 - 1 = 4x

4 = 4x => x = 4÷4 =1

x = 1.

y = -2x + 4

C.(1, 2)

y = - 2(1) + 4

y = - 2 + 4 = 2

y = 2.

2 = -2x + 4

2 - 4 = - 2x

- 2 = - 2x => x = 2÷2 = 1

x = 1.

y = 4x + 1

D.(1/4, 2)

y = 4(1/4) + 1

y = 4(0.25) + 1

y = 1 + 1 = 2

y = 2.

y = 4x + 1

2 = 4x + 1

2 - 1 = 4x

1 = 4x => x = 1/4

Point A is the point of intersection of the lines.

Answer 2

Explanation:

y = 4x + 1 and y = -2x + 4

4x + 1 = -2x + 4, 6x = 3, x = 0.5

When x = 0.5, y = 4(0.5) + 1 = 3.

The point of intersection is (0.5, 3). (B)