Solving Systems of Linear Equations by Graphing

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more equations with the same variables.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system.

Front

How can you determine the solution to a system of equations graphically?

Back

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

Front

What is the ordered pair for the intersection of the lines y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What does the term 'ordered pair' refer to in the context of linear equations?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on the Cartesian plane.

Front

If a system of equations has no solution, what does that imply about the lines on a graph?

Back

It implies that the lines are parallel and will never intersect.

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, indicating the value of y when x = 0.

Front

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

Back

Substitute the x and y values of the point into each equation to see if they hold true.

Front

What is the graphical representation of the equation y = 3x - 2?

Back

A straight line with a slope of 3 and a y-intercept of -2.

Front

What does it mean if two lines in a system of equations intersect at one point?

Back

It means there is exactly one solution to the system.