Solving Linear Systems (Substitution)

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a linear system?

Back

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method?

Back

The substitution method is a technique for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform algebraic operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

Given the equation y = 2x - 4, what is y when x = 1?

Back

y = 2(1) - 4 = 2 - 4 = -2.

Front

What is the first step in using the substitution method?

Back

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

Front

If y = 2x - 4, what is the value of y when x = -1?

Back

y = 2(-1) - 4 = -2 - 4 = -6.

Front

What is the solution to the system of equations: y = 2x - 4 and 7x - 2y = 5?

Back

The solution is (-1, -6).

Front

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

Back

A system of equations is consistent if it has at least one solution.

Front

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

Back

A system of equations is inconsistent if it has no solutions.