Question

How many solutions does the system have?

21x + 6y = 42

7x + 2y = 14

Choose one answer:

1. Exactly one solution.

2. No solutions.

3. Infinitely many solutions.

Answer 1

For this case we have the following system of equations:

$21x + 6y = 42\\7x + 2y = 14$

We multiply the second equation by -3:

$-21x-6y = -42$

Thus, we observe that the second equation is equivalent to the first, if we add both we get:

$21x-21x + 6y-6y = 42-42\\0 = 0$

The equality is fulfilled. The lines are on top of each other.

Answer:

Infinite solutions

Answer 2

Answer:

System of equations: 3. Infinitely many solutions.

Graph: 2. No solutions.

Step-by-step explanation:

If you solve the equation system using a graph, then the solution is to intersect the line.

The graph has two parallel lines (no intersection). Therefore, this system of equations has no solutions.

Algebraic solution:

21x + 6x = 42    divide both sides by (-3)

-7x - 2x = -14

Add both equations by sides:

   7x + 2y = 14

+ -7x - 2y = -14

           0 = 0        TRUE

Therefore the system of equations has Infinitely many solutions.