Review Solving Linear Systems by Graphing and Substituion

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

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through the points.

Front

What does it mean if two lines intersect at a point?

Back

If two lines intersect at a point, it means there is one unique solution to the system of equations represented by those lines.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, it means there is no solution to the system of equations, as the lines never intersect.

Front

What does it mean if two lines coincide?

Back

If two lines coincide, it means there are infinitely many solutions to the system, as every point on the line is a solution.

Front

How can you determine the solution of a system of equations graphically?

Back

You can determine the solution graphically by finding the point(s) where the lines representing the equations intersect.

Front

What is the first step in the substitution method?

Back

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

Front

What is the solution to the system: y = 3x and 2x - 3y = 14?

Back

The solution is (-2, -6).