Question

How many solutions does the system of equations below have?y = -10x + 7/3y = -10x + 1/10No solutionOne solutionInfinitely many solutions

Answer 1

We re-write the system of equations by using the fact that we need the y-values to be the same, so we equal them:

- 10 x + 7/3 = - 10 x + 1/10

We notice then, as we try to solve for the one unknown left (x), that as we add 10 x on both sides of our new equation, all the terms in "x" go away, as shown below:

- 10 x + 10 x + 7/3 = - 10 x + 10 x + 1/10

combine like terms:

7/3 = 1/10

so we notice we have ended up with a ridiculous solution, a statement that tells us that 7/3 equals 1/10 which is mathematically a FALSE statement. Therefore, we conclude that the system has NO solutions, given that there are no possible x or y values that can ever produce a logical answer.

We select therefore the option No solution, among the list of answers.