Check If X Satisfies an Equation

How do you check to see if an Ordered Pair is a solution to a System of Linear Equations?

• Plug in the x-value and y-value to see if each equation works

• Take a random guess

• Solve each equation for x and then use Inverse Operations

• Multiply the Slope of each line by the Constant of Proportionality

Is (1,9) a solution for the following System? Explain why or why not.

y = 5x + 4

y = -6x + 15

Evaluate responses using AI:

OFF

Is (4, 5) a solution to the system of equations?
4x+y=21
-3x-6y=10

• Yes, it is a solution to the system of equations

• No, it only satisfies the first equation, and fails to satisfy the second.

• No, it only satisfies the second equation, and fails to satisfy the first.

• No, it fails to satisfy both equations

Use the graph to solve the equation.

x = _____

Mathematical Equivalence

ON

Does the solution (6, -2) satisfy the equation 3x - 4y = 24

• Yes

• No

Problem #56

Correct the error in solving the equation.

• x = 2

• x = -6

Describe the error in solving the equation.

• The solutions should be checked because x = -6 is extraneous & should not be listed as a solution.

• Both solutions satisfy the original equation. So, there are no extraneous solutions.

Determine whether the given value of the variable is a solution.
x + 6 = 14, when x = 8

• yes

• no

Determine whether the given value of the variable is a solution.
3a = 18, when a = 6

• yes

• no

Which equation has a solution of 12?

• x - 6 = 6

• x + 6 = 6

• 4 = x - 16

• 4 = 8 + x