Solving 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 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: 6x + y = -1 and y = -3x - 4?

Back

Substitute -3x - 4 for y in the first equation.

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 is the solution to the system: y = 2x - 11 and -3y = -6x - 15?

Back

No solution, as the equations represent parallel lines.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the solution to the system: y + 3x = 11 and 5x + y = 21?

Back

(5, -4), which means x = 5 and y = -4.

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 the line is a solution.

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.