Question

Tell whether the system has one solution, no solution, or infinitely many solutions. Y = 3x + 4 –12x + 4y = 16

Answer 1

Infinitely many solutions.

Explanation:

(1) y = 3x + 4

(2) -12x + 4y = 16 Substitute (1) into (2)

-12x + 4(3x + 4) = 16 Distribute the 4

-12x + 12x + 16 = 16 Combine like terms

16 = 16

There are infinitely many solutions.

In the diagram belo, you can see the orange graph of Equation (1) behind the dashed blue line of equation (2). The two lines coincide with each other.