RETEST - Unit 5: Systems of Equations

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 point(s) where the equations intersect.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations do not intersect at any point.

Front

What is the substitution method for solving systems of equations?

Back

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

Front

What is the elimination method for solving systems of equations?

Back

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

Front

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

Back

(1, 3)

Front

What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

(3, 1)

Front

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

Back

(2, -4)

Front

How can you represent a system of equations using matrices?

Back

A system of equations can be represented in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.