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

What does it mean for a system of equations to have no solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

(-2, -1)

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

How can you check your solution for 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 a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.