Question

Consider the system of equations shown.

{y=x+11
−y=−x+11

What is the solution to this system of equations?

Responses

A.(0,11)

B.( 0 , 11 )

C.no solution

D.infinitely many solutions

Answer 1

C. no solution

Explanation:

You want to know the solution to the system of equations ...

• y = x + 11
• -y = -x + 11

Comparing equations

Equations are best examined for the possible number of solutions when they are written in the same form. Here, we can put both equations into slope-intercept (y=) form by multiplying the second equation by -1.

-y = -x + 11 . . . . . . . .second equation

y = x - 11 . . . . . . . . equivalent equation; multiplied by -1

Now, you see that these slope-intercept equations have the same slope (x-coefficient = 1), but different intercepts (11, -11).

• y = x + 11
• y = x - 11 . . . . . rewritten 2nd equation

Parallel lines

Lines with the same slope and different intercepts are parallel lines. They never meet, so never have any points in common. There are no values of x and y that satisfy both equations at the same time.

There are no solutions.

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