Question

Classify the system of equations and identify the number of solutions.

2x + y = 7
y + 5 = −2x
inconsistent, dependent; one
consistent, independent; one
inconsistent; none
consistent, dependent; infinite

Answer 1

2x+y=7

• y=-2x+7

y+5=-2x

• y=-2x-5

Slopes are equal lines are parallel,no solutions

Option C

Answer 2

• C. Inconsistent; none

Explanation:

Given system:

• 2x + y = 7 ⇒ y = -2x + 7
• y + 5 = -2x ⇒ y = -2x - 5

We observe that:

• The slopes are same m = -2
• The y-intercepts are different, b = 7 and b = - 5
• The lines are parallel, so no solution

Correct choice is C