Question

4. Four systems of equations are shown in the table. Indicate whether each system has no solution, one

solution, or infinitely many solutions. Select one answer in each row.
Infinitely Many
No Solution
One Solution
Solutions
y = 3x + 1
y = 3x + 5
y = 2x + 2
y = -2x + 4
3x + 2y = 2
3x + 2y = 5
x - 2y = 1
2x - 4y = 2

Answer 1

• y = 3x + 1
• y = 3x + 5

No solution, parallel lines as same slope of 3

• y = 2x + 2
• y = -2x + 4
• 2x+2= -2x+4 ⇒ 4x=2 ⇒ x= 1/2

One solution

• 3x + 2y = 2 ⇒ y= -1.5x+1
• 3x + 2y = 5 ⇒ y= -1.5x+5

No solution, parallel lines as same slope of -1.5

• x - 2y = 1
• 2x - 4y = 2 ⇒ x- 2y= 1

Infinitely many solutions as 2 overlapping lines