Solve Systems by Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean to solve a system of equations by substitution?

Back

Solving a system of equations by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is a zero pair in mathematics?

Back

A zero pair consists of two numbers that add up to zero, such as 5 and -5.

Front

What is the opposite of negative in terms of numbers?

Back

The opposite of negative is positive.

Front

How do you find the value of y in the equation y = 3x - 5 when x = 1?

Back

Substituting x = 1 into the equation gives y = 3(1) - 5 = -2.

Front

What is the solution to the system of equations 2x + 4y = -6 and y = 3x - 5?

Back

The solution is (1, -2).

Front

What is the first step in solving the system of equations using substitution?

Back

The first step is to solve one of the equations for one variable.

Front

If x = 6, what is the value of y in the equation y = 2x - 3?

Back

Substituting x = 6 gives y = 2(6) - 3 = 9.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the point(s) where the lines representing the equations intersect.