Verify Solutions of Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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 to verify a solution of a linear equation?

Back

Verifying a solution means substituting the given coordinates into the equation to check if the equation holds true.

Front

How do you substitute coordinates into a linear equation?

Back

To substitute coordinates (x, y) into a linear equation, replace x with the x-coordinate and y with the y-coordinate, then simplify to see if the equation is true.

Front

What is the solution to the equation 2x - 3y = -7 when x = 5 and y = 1?

Back

Substituting x = 5 and y = 1 gives 2(5) - 3(1) = 10 - 3 = 7, which does not equal -7. Therefore, (5, 1) is not a solution.

Front

What is the solution to the equation -3x + 4y = 8 when x = 0 and y = -2?

Back

Substituting x = 0 and y = -2 gives -3(0) + 4(-2) = 0 - 8 = -8, which does not equal 8. Therefore, (0, -2) is not a solution.

Front

What is the solution to the equation 5x - 2y = -13 when x = -1 and y = 4?

Back

Substituting x = -1 and y = 4 gives 5(-1) - 2(4) = -5 - 8 = -13, which equals -13. Therefore, (-1, 4) is a solution.

Front

What is the solution to the equation 2x - 3y = 5 when x = 0 and y = 0?

Back

Substituting x = 0 and y = 0 gives 2(0) - 3(0) = 0, which does not equal 5. Therefore, (0, 0) is not a solution.

Front

What is the solution to the equation 4x + 2y = 2 when x = -2 and y = 3?

Back

Substituting x = -2 and y = 3 gives 4(-2) + 2(3) = -8 + 6 = -2, which does not equal 2. Therefore, (-2, 3) is not a solution.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

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

Back

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