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, how do you substitute y in another equation?

Back

You replace y in the other equation with the expression 2x - 4.

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, if it is not already solved.

Front

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

Back

When x = -1, 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 solution to be a point of intersection?

Back

A solution is a point of intersection if it represents the coordinates where the graphs of the equations meet.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.