Check and Graph Solutions to Two-Variable Equations

• Infinite number of solutions

• (7, 5)

• (-1, 5)

• No Solution

• (-3, -8)

• (-8, 3)

• (2, 3)

• (-8, -6)

Which graph represents a system of equations with infinite solutions?

• 
• 
• 
• None of the above

The graph of the linear equation in two variables y = mx is _____

• a line parallel to x - axis 

• a line parallel to y - axis 

• a line passes through the origin

• not a straight line

Which graph represents a system of equations with no solution?

• 
• 
• 
• None of the above

How many solutions does the system of equations have?

• One solution

• No solution

• Infinite solutions

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)

• (1, -4)

• (-4, 1)

• (4, -1)

Solve the system of equations using substitution:
-4x + 4y = 8
y = -2x - 10

• (-4, -2)

• (12, -34)

• (4, -18)

• (-2, -6)

• No Solution

• (2, 2)

• (-1, 2)

• (-1, -2)

Which has the correct order of steps for solving systems by substitution?

• 1. Isolate a variable ex. Change 3y + x = 3 to x = -3y + 3
  2. Substitute and solve for a variable ex. y = 3x + 2 plug (3x + 2) into y in the other equation to solve for x
  3. Substitute the value of a variable you already solved for and solve for the remaining variable ex. use x = 3 plug it in 3(3) + y = 0 and solve y = -9
  4. Check your solution! ex. solution is (3, 5) plug it in to your original equations and see if they are true.

• 1. Check your solution! ex. solution is (3, 5) plug it in to your original equations and see if they are true.
  2. Isolate a variable ex. Change 3y + x = 3 to x = -3y + 3
  3. Substitute and solve for a variable ex. y = 3x + 2 plug (3x + 2) into y in the other equation to solve for x
  4. Substitute the value of a variable you already solved for and solve for the remaining variable ex. use x = 3 plug it in 3(3) + y = 0 and solve y = -9

• 1. Isolate a variable ex. Change 3y + x = 3 to x = -3y + 3
  2. Substitute and solve for a variable ex. y = 3x + 2 plug (3x + 2) into y in the other equation to solve for x
  3. Substitute the value of a variable you already solved for and solve for the remaining variable ex. use x = 3 plug it in 3(3) + y = 0 and solve y = -9
  4. Don't check your solution, you are always right

• Shen Yun