Is the point a solution to the system?

Front

What is a solution to a system of equations?

Back

A solution is a set of values for the variables that makes all equations in the system true.

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 satisfies an equation?

Back

It means that when the x and y values of the point are plugged into the equation, the equation holds true.

Front

What is the first step to check if (4, 1) is a solution for the system y = -x + 5 and y = 2x - 7?

Back

Substitute x = 4 and y = 1 into both equations.

Front

Is (4, 1) a solution for the system y = -x + 5 and y = 2x - 7?

Back

Yes, it satisfies both equations.

Front

What is the result of substituting (-3, -7) into the equations y = 4x + 5 and y = x - 4?

Back

Both equations are true, so (-3, -7) is a solution.

Front

What happens if a point does not satisfy one of the equations in a system?

Back

The point is not a solution to the system.

Front

What is the significance of the coordinates (x, y) in a system of equations?

Back

They represent a specific point in the coordinate plane that may or may not satisfy the equations.

Front

What does it mean if a point is a solution to a system of equations?

Back

It means that the point lies at the intersection of the lines represented by the equations.

Front

How can you verify if (2, -1) is a solution to the system y = 5x + 3 and y = -2x - 4?

Back

Substitute x = 2 and y = -1 into both equations; it does not satisfy both.