Question

Select all the systems of equations that have exactly one solution.

Thank you so much for your help

Answer 1

A. {y = 3x + 1 y =− 3x + 7

B. {y = 3x + 1 y = x + 1

Explanation:

The required options are

A. {y = 3x + 1 y =− 3x + 7

B. {y = 3x + 1 y = x + 1

C. {y = 3x + 1 y = 3x + 7

D. {x + y = 10 x + y = 12

For option A

y = 3x + 1 and y =− 3x + 7

Equating both expression

3x+1 = -3x+7

3x+3x = 7-1

6x = 6

x = 6/6

x = 1

Since y = 3x+1

y = 3(1)+1

y = 4

For y = 3x + 1 and y = x + 1

Equate both expression

3x+1 = x+1

3x-x = 1-1

2x = 0

x = 0

Substitute x = 0 into y= x+1

y = 0+1

y = 1

c) {y = 3x + 1 and y = 3x + 7

Equate both expression

3x+1 = 3x+7

3x - 3x = 7-1

0x = 6

x = 6/0

X = infinity

the roots have infinite number of solutions

d) x + y = 10.... 1

x + y = 12 .... 2

Add both equations

2x+2y = 22

x+y = 11

Since we have one equation with tei unknown hence the equation has infinite number of solutions

The correct answers are A and B