Solving Systems: Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations 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 system of equations y = 3x - 14 and y = x - 10 using substitution?

Back

1. Set the equations equal: 3x - 14 = x - 10. 2. Solve for x: 2x = 4, so x = 2. 3. Substitute x back into one equation: y = 3(2) - 14 = -8. The solution is (2, -8).

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

What is the first step in using substitution to solve a system of equations?

Back

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

Front

How do you determine if a solution is correct after solving a system of equations?

Back

Substitute the values of the solution back into the original equations to verify that both equations are satisfied.

Front

What is the solution to the system of equations x = y + 7 and y = 8 + 2x?

Back

1. Substitute x in the second equation: y = 8 + 2(y + 7). 2. Solve for y: y = -22. 3. Substitute y back to find x: x = -15. The solution is (-15, -22).

Front

What does it mean if the solution of a graph is (2, 0)?

Back

It means that the point (2, 0) is the intersection of the two lines represented by the equations in the system.

Front

How do you solve the system of equations y = 4x - 3 and y = 2x + 13 using substitution?

Back

1. Set the equations equal: 4x - 3 = 2x + 13. 2. Solve for x: 2x = 16, so x = 8. 3. Substitute x back into one equation: y = 4(8) - 3 = 29. The solution is (8, 29).

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation is two parallel lines that do not intersect.

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, where both equations are satisfied simultaneously.