How Many Solutions | Math Coach Amy

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Key Ideas Together Independent Practice

Determine the number of solutions for the system of equations:

y = x + 2

y = −2x + 8

1 solutions

0 solutions

overlapping lines, infinite solutions

Desmos graph of y = x + 2 and y = −2x + 8. The lines cross once.

The lines cross once, Exactly one solution.

Together

Work these three in a session.

Determine the number of solutions for the systems of equations.

y = 2x + 1

y = −x + 7

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = 2x + 1 and y = −x + 7. The lines cross once.

The lines cross once, Exactly one solution.

Answer: B. Exactly one solution

Determine the number of solutions for the systems of equations.

y = 3x + 4

y = 3x − 2

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = 3x + 4 and y = 3x − 2. The lines never cross.

The lines are parallel, No solution.

Answer: A. No solution

Determine the number of solutions for the systems of equations.

y = −2x + 5

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = −2x + 5 and y = −2x + 5. The equations draw the same line.

The lines overlap, Infinitely many solutions.

Answer: D. Infinitely many solutions

Independent

Independent Practice

Try these five on your own.

Determine the number of solutions for the systems of equations.

y = 3x − 4

y = x + 2

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = 3x − 4 and y = x + 2. The lines cross once.

The lines cross once, Exactly one solution.

Answer: B. Exactly one solution

Determine the number of solutions for the systems of equations.

y = −x + 6

y = −x − 1

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = −x + 6 and y = −x − 1. The lines never cross.

The lines are parallel, No solution.

Answer: A. No solution

Determine the number of solutions for the systems of equations.

y = −3x + 1

y = −x − 5

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = −3x + 1 and y = −x − 5. The lines cross once.

The lines cross once, Exactly one solution.

Answer: B. Exactly one solution

Determine the number of solutions for the systems of equations.

y = 2x − 6

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = 2x − 6 and y = 2x − 6. The equations draw the same line.

The lines overlap, Infinitely many solutions.

Answer: D. Infinitely many solutions

Determine the number of solutions for the systems of equations.

y = x + 8

y = x − 3

A. No solution B. Exactly one solution C. Exactly two solutions D. Infinitely many solutions

Show Answer

Desmos graph of y = x + 8 and y = x − 3. The lines never cross.

The lines are parallel, No solution.

Answer: A. No solution

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