Solutions to 2-Variable Equations

Front

What is a solution to a 2-variable equation?

Back

A solution to a 2-variable equation is an ordered pair (x, y) that makes the equation true when substituted for x and y.

Front

How do you determine if an ordered pair is a solution to an equation?

Back

Substitute the x and y values of the ordered pair into the equation. If both sides of the equation are equal, then it is a solution.

Front

What does the equation 2x + 3y = 10 represent?

Back

It represents a linear relationship between x and y, where the graph of the equation is a straight line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 4x - 7?

Back

The y-intercept is -7, which is the value of y when x = 0.

Front

What does it mean if an ordered pair is not a solution to an equation?

Back

It means that substituting the values of the ordered pair into the equation does not satisfy the equation.

Front

How can you find the x-intercept of the equation 5x - 2y = 18?

Back

Set y = 0 and solve for x. The x-intercept is the point where the graph crosses the x-axis.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope of the line and how steeply it rises or falls.

Front

What is an example of an ordered pair that is a solution to the equation y = 3x + 5?

Back

(2, 11) is a solution because when x = 2, y = 3(2) + 5 = 11.

Front

What is the general form of a linear equation in two variables?

Back

The general form is Ax + By = C, where A, B, and C are constants.