Tell if the point is a solution

Front

What is a solution to a system of equations?

Back

A solution is an ordered pair (x, y) that satisfies all equations in the system.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

Front

What does it mean if a point does not satisfy an equation?

Back

It means that when you substitute the point's coordinates into the equation, the equation does not hold true.

Front

What is the ordered pair for the point (4, -1)?

Back

The ordered pair is (4, -1), where 4 is the x-coordinate and -1 is the y-coordinate.

Front

If a point (x, y) satisfies the equation y = 5x + 3, what does that imply?

Back

It implies that when you substitute x into the equation, the resulting y value equals the y-coordinate of the point.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common.

Front

What is the graphical representation of a solution to a system of equations?

Back

The solution is represented by the point where the graphs of the equations intersect.

Front

What is the difference between a solution and a non-solution?

Back

A solution satisfies all equations in the system, while a non-solution does not satisfy at least one equation.

Front

How can you verify if (-3, -7) is a solution to the equations y = 4x + 5 and y = x - 4?

Back

Substitute x = -3 into both equations and check if y equals -7 for both.