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 in solving linear systems?

Back

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform 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 + 1, what is y when x = 1?

Back

y = 2(1) + 1 = 3.

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

Back

y = 4(2) - 1 = 7.

Front

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

Back

The solution is (1, 3).

Front

How do you check if a solution is correct for a linear system?

Back

Substitute the solution values into both equations to see if they hold true.

Front

What is the graphical representation of a linear system?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.