Solution Types Algebraically Systems

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Answer explanation

These lines intersect at ONE point. This means that only one point will be true for the equations of both lines.

Solve the following systems of equations using substitution:

x = 6

y = 2x - 3

• (6, 6)

• (6, 9)

• (9, 6)

• (9, 9)

Answer explanation

When solving a system of equations algebraically, which statement results in no solution?

• 4 = 7

• -2 = 2

• -3 = 3

• all of the above

Answer explanation

You will be left with a contradiction (something false) when trying to solve a system of equations, if there is no solution.

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Answer explanation

The lines overlap everywhere, so they have the same equation.

This means the solutions for one equation are also the solutions for the other.

The lines go on infinitely in both directions, so there are an infinite number of points that are shared solutions.

Solve using elimination.

• (4,5)

• (3,4)

• (5,4)

Solve using substitution.

• (1,3)

• (3,-1)

• (7,3)

Solve using the most efficient method.

• (2,1)

• (1,-2)

• (2,-1)

Solve using your preferred method.

• (3,7)

• (5,7)

• (6,6)

Solve using the most efficient method.

• (3,4)

• (4,12)

• (14,17)

Solve using your preferred method

• (14,10)

• (2,10)

• (4,14)