Solving Systems by Graphing and Substitution

Front

What is a system of linear equations?

Back

A set of 2 or more equations that share the same variables.

Front

What does it mean if two lines overlap each other in a system of equations?

Back

It means the system has infinitely many solutions.

Front

How do you solve a system of equations by graphing?

Back

You graph both equations on the same coordinate plane and find the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in using substitution to solve the system: y = 2x + 3 and 3x + y = 12?

Back

Substitute 2x + 3 for y in the second equation.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

It means the system has no solutions, as the lines never intersect.

Front

If the solution to a system of equations is (3, -4), what does this point represent?

Back

It represents the point where both equations are true simultaneously.

Front

What is the graphical representation of the equation y = -2x + 5?

Back

A straight line with a slope of -2 and a y-intercept of 5.

Front

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

Back

By substituting the point's coordinates into both equations and checking if they hold true.

Front

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

Back

It is the point where the line crosses the x-axis, meaning y = 0.