Question

Write a second equation for the system so it has infinitely many solutions.

Write a second equation whose graph goes through (0,2) so that the system has no solutions.

Write a second equation whose graph goes through (2,2) so that the system has one solution at (4,3).

Answer 1

See below ↓

Explanation:

Our equation :

• y = 3/2x - 3

(A) Infinitely Many Solutions

• y = 3/2x - 3
• The slope and y-intercept have to be equal in order for it to have infinitely many solutions

(B) No solution

• y = 3/2x + 1
• The slope has to be equal and the y-intercept has to be different in order for it to have no solution

(C) One solution at (4, 3)

• x has to equal 4
• y = 3/2x - 3 and y = 2x - 1
• In both of these equations, (4, 3) is a solution