Solving systems of equations by substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

What does it mean to solve a system of equations by substitution?

Back

Solving a system of equations by substitution 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 algebraic operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the first step in solving the system of equations y = -6x + 5 and -2x + y = 5 by substitution?

Back

The first step is to solve one of the equations for y or x. In this case, y is already isolated in the first equation.

Front

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

Back

The solution is (1, 3), which means x = 1 and y = 3.

Front

What does it mean if two lines represented by equations are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system of equations.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.

Front

What is the significance of the point (0, 5) in the context of the equations y = -6x + 5 and -2x + y = 5?

Back

The point (0, 5) is the intersection of the two lines represented by the equations, indicating that it is the solution to the system.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.