Question

A system is described by the equations2x + 3y = 104x + By = 20For what value of B will the system have infinitely many solutions?

Answer 1

Kellurz, this is the solution:

2x + 3y = 10

4x + By = 20

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Isolating x in the first equation:

2x + 3y = 10

2x = 10 - 3y

Dividing by 2:

2x/2 = (10 - 3y)/2

x = (10 - 3y)/2

Substituting x and solving for y in the second equation:

4x + By = 20

4 * (10 - 3y)/2 + By = 20

40 - 6y + By = 20

-6y + By = 20 - 40

-6y + By = -20

Now, we can solve for B, using the following ratios:

2/4 = 3/B = 10/20

1/2 = 3/B = 1/2

1/2 = 3/B

B = 6