M7D3 Solving Linear Systems Using Substitution

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to solve a system of equations?

Back

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

Front

What is substitution in solving linear systems?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you identify the solution of a system of equations graphically?

Back

The solution of a system of equations is the point where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating that there is no solution to the system.

Front

What does it mean if two lines are the same in a system of equations?

Back

If two lines are the same, it means they have infinitely many solutions, as every point on the line is a solution.

Front

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

Back

If two lines intersect at one point, it means the system has a unique solution, which is the coordinates of the intersection point.

Front

How do you solve the equation x - 2y = 2 for x?

Back

To solve for x, rearrange the equation: x = 2 + 2y.

Front

How do you solve the equation 3x + 4y = 3 for y?

Back

To solve for y, rearrange the equation: 4y = 3 - 3x, then y = (3 - 3x)/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 in terms of the other variable.