Question

Solve the system, using substitution.

y = 1 - 5x and 5x + y = 8
A. no solution
B. infinitely many solutions

Answer 1

Substitution means that we substitute a variable (In this case y) for an equation.

Basically, we know 5x + y = 8, and we also know the value of y! The equation tells us that y = 1 - 5x. So we can substitute this in, like so.

5x + y = 8
5x + (1 - 5x) = 8.

The brackets shouldn't go in for a real question. I'm just putting them in to show you exactly what's being substituted. In a real question, you should write it like this:

5x + 1 - 5x = 8.

Now we have 5x and a -5x, so those add up to nothing.

1 = 8.

Because 1 does not, in fact, equal 8, this question has no solutions.