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 of equations 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 by itself.

Front

What is the first step in solving the system: y = 6x - 11 and y = -x + 3?

Back

Set the two equations equal to each other: 6x - 11 = -x + 3.

Front

What is the solution to the system: y = 3x - 8 and y = 4 - x?

Back

The solution is (3, 1).

Front

What does it mean if two equations represent the same line?

Back

If two equations represent the same line, they have infinitely many solutions, as every point on the line is a solution.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane and finding the intersection points.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

What is the solution to the system: -5x - y = 21 and y = 4x + 6?

Back

The solution is (-3, -6).

Front

What happens if the lines represented by a system of equations are parallel?

Back

If the lines are parallel, the system has no solution, as they never intersect.