Solving Systems of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

The system has infinitely many solutions because the lines are the same.

Front

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

Back

The solution is the point where the two lines intersect on the graph.

Front

What is the y-coordinate of the solution to the system of equations x - 2y = 1 and x + 4y = 7?

Back

1

Front

Solve for x and y: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)