Solving Systems by Graphing and Substitution

Front

What is the solution to a system of equations?

Back

The solution (x, y) is the point where the equations intersect.

Front

What does it mean if two lines in a system of equations do not intersect?

Back

It means there is no solution to the system.

Front

How do you solve a system of equations using substitution?

Back

You solve one equation for one variable and substitute that expression into the other equation.

Front

What is the first step in solving the system of equations y = 4x - 6 and 5x - y = 9 by substitution?

Back

Substitute y from the first equation into the second equation.

Front

What is the solution to the system of equations y = -3x + 11 and 5x + y = 21?

Back

(5, -4) is the solution.

Front

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

Back

It means the equations represent the same line.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the significance of the intersection point of two lines in a system of equations?

Back

It represents the values of x and y that satisfy both equations.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.