Solve by Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you solve the equation y = -x - 10 and y = 4x using substitution?

Back

1. Solve y = 4x for x: x = -y/4. 2. Substitute into y = -x - 10: y = -(-y/4) - 10. 3. Solve for y: y = 4 - 10 = -6. 4. Substitute y back to find x.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

Front

What does it mean for two equations to be inconsistent?

Back

Two equations are inconsistent if they have no solutions, meaning their graphs are parallel and never intersect.

Front

What is the first step in solving a system of equations by substitution?

Back

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

Front

If y = x - 9 and y = -9, what are the values of x and y?

Back

x = 9, y = -9.

Front

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

Back

Substitute the values of the variables back into the original equations to see if both equations are satisfied.

Front

What is the solution to the system of equations y = x + 6 and y = 3?

Back

x = -3, y = 3.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy both equations.

Front

How do you solve the equations y = -x - 14 and y = -8x using substitution?

Back

1. Set -x - 14 = -8x. 2. Solve for x: 7x = -14, x = -2. 3. Substitute x back to find y: y = -(-2) - 14 = -16.