Solving Systems of Equations with Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

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

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope is -3.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the solution to the system of equations: y = x + 2 and y = -x + 4?

Back

(1, 3) - The lines intersect at the point (1, 3).

Front

What is the solution to the system of equations: y = 2x + 3 and y = 2x - 1?

Back

No solution - The lines are parallel.