Unit 8.3 Lesson 10: Solutions to Linear Equations Practice

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What does it mean for a point to be a solution to a linear equation?

Back

A point (x, y) is a solution to a linear equation if, when the x and y values are substituted into the equation, the equation holds true.

Front

How do you determine if (1, 2) is a solution to the equation 2x + 5y = 12?

Back

Substitute x = 1 and y = 2 into the equation: 2(1) + 5(2) = 2 + 10 = 12. Since the equation is true, (1, 2) is a solution.

Front

What is the process to check if a point is a solution to a linear equation?

Back

To check if a point (x, y) is a solution, substitute the x and y values into the equation and see if the left side equals the right side.

Front

Is (3, 1) a solution to the equation 4x + 3y = 12?

Back

No, substituting gives 4(3) + 3(1) = 12 + 3 = 15, which does not equal 12.

Front

What are the coordinates of a point?

Back

The coordinates of a point are written as (x, y), where x is the horizontal position and y is the vertical position on a graph.

Front

What does it mean for a point to not be a solution to a linear equation?

Back

A point is not a solution if substituting its coordinates into the equation does not satisfy the equation.

Front

Identify the solution pair from the options: (2,1) and (0,-4), (1,2) and (4,0), (2,1) and (0,4), (1,2) and (0,4).

Back

The solution pair is (2,1) and (0,4) for the equation 2x + 5y = 12.

Front

Which point is not a solution to the equation: (0,0), (3,-5), (-2,3), (-5,3)?

Back

The point (-5,3) is not a solution.

Front

Is (5, 5) a solution to the equation x + y = 12?

Back

No, substituting gives 5 + 5 = 10, which does not equal 12.