Systems- Substitution

Front

What is the substitution method in solving systems of equations?

Back

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

Front

How do you identify which equation to solve first in the substitution method?

Back

Choose the equation that is easiest to solve for one variable, typically the one with a coefficient of 1 or -1.

Front

What is the first step in using the substitution method?

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and 4x + y = 11, how would you solve using substitution?

Back

Substitute y from the first equation into the second: 4x + (2x + 3) = 11, then solve for x.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

Solve the system using substitution: y = 3x + 1 and 2x - y = 4. What is the solution?

Back

The solution is (1, 4).

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the point(s) where the equations intersect, indicating the values of the variables that satisfy both equations.

Front

How can you check your solution after using the substitution method?

Back

Substitute the values back into both original equations to verify that they hold true.

Front

What is a common mistake when using the substitution method?

Back

A common mistake is incorrectly substituting the expression for the variable, leading to wrong calculations.