Linear Equations with One, None, and Infinitely Many Solutions

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

This system has _____ solutions.

• 0

• 1

• 2

• Infinitely many

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
5x + 6 = 2 + 3x

• one

• no solutions

• infinite solutions

What is the solution to the equations?

• one solution

• no solution

• infinite solutions

• none of these

Fill in the blanks so the equation has infinitely many solutions.

7x + 2 + x = ​ (a)   (2x + ​ ​ (b)   ​ )

• 4

• 2

• 6

• 8

Solve the system using substitution.
16x + 2y = 2
y = -8x - 1

• (2,3)

• (-3,7)

• No Solution

• Infinitely Many Solutions

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines