Solve Systems by Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system by substitution?

Back

Solving a system by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

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

Front

What is the first step in solving the system: x + 2y = 2 and x = -4y + 2?

Back

The first step is to substitute -4y + 2 for x in the first equation.

Front

What is the solution to the system: y = -6x + 5 and -2x + y = 5?

Back

The solution is (0, 5).

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 do not intersect at any point.

Front

What is the substitution method?

Back

The substitution method is a technique for solving systems of equations by expressing one variable in terms of the other and substituting it into the second equation.

Front

Solve the system by substitution: 5x + 4y = -14 and y = -7x - 15. What is the solution?

Back

The solution is (-2, -1).

Front

What is the second equation after substituting 4x - 11 for y in -4x + 3y = -1?

Back

The second equation becomes -4x + 3(4x - 11) = -1.