Solving 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, you manipulate the equation using algebraic operations (addition, subtraction, multiplication, division) to get the variable on one side of the equation by itself.

Front

Solve for y: x = 2y + 4

Back

y = (x - 4)/2

Front

If y = 2x + 3, what is y when x = 1?

Back

y = 5

Front

What is the first step in solving the system: 2x + 3y = 6 and y = x - 2?

Back

Substitute x - 2 for y in the first equation.

Front

Solve the system using substitution: y = 4x - 1 and 2x + y = 5.

Back

(2, 7) because substituting y gives 2x + (4x - 1) = 5.

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

Solve the system: x = 3y + 1 and 2x - y = 4.

Back

(3, 1) after substituting x in the second equation.

Front

What is the solution to the system: y = 2x + 1 and y = -x + 4?

Back

(1, 3) after setting the equations equal to each other.

Front

How do you check your solution in a system of equations?

Back

Substitute the values of the variables back into the original equations to see if they hold true.