Solving Systems of Equations (All Methods)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

What are the three methods to solve a system of equations?

Back

The three methods are: 1) Graphing, 2) Substitution, 3) Elimination.

Front

How does the elimination method work?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

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

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

(2, 5)

Front

When solving a system of equations, does the method used affect the solution?

Back

No, using any method will result in the same correct solution.

Front

Solve this system by substitution: y = 2x + 1 and 3x - y = 4.

Back

(1, 3)

Front

Solve for x and y: 5x + 3y = 7 and y = 4.

Back

(-1, 4)