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 y = 4x + 9?

Back

Set y to 0 and solve for x: 0 = 4x + 9, which gives x = -9/4.

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 x + 7y = 17?

Back

(10, 1) is a solution because substituting gives 10 + 7(1) = 17.

Front

What does the term 'ordered pair' mean in mathematics?

Back

An ordered pair is a pair of numbers (x, y) where the first number represents the x-coordinate and the second number represents the y-coordinate.