Solve systems 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 isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

Solve the system by substitution: x + 2y = 2, x = -4y + 2

Back

(2, 0)

Front

Solve the system by substitution: 5x + 4y = -14, y = -7x - 15

Back

(-2, -1)

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

How can you check your solution after solving a system of equations?

Back

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

Front

Solve the system by substitution: 2x + 3y = 6, y = 2 - x

Back

(0, 2)

Front

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

Back

Choose one equation and solve for one variable in terms of the other variable.