Systems of Equations--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 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.

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

Given the equations 3x + 2y = 16 and y = -7x + 19, what is the first step in using substitution?

Back

First, substitute the expression for y from the second equation into the first equation.

Front

What is the solution to the system 3x + 2y = 16 and y = -7x + 19?

Back

The solution is (2, 5).

Front

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

Back

Substitute the solution back into both original equations. If both equations are true, the solution is correct.

Front

What does it mean if two lines represented by equations are parallel?

Back

If two lines are parallel, they have no points of intersection, meaning there is no solution to the system of equations.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the values of the variables that satisfy all equations in the system.

Front

Given the equations y = 5x - 5 and y = -4x + 22, how do you find the solution using substitution?

Back

Set the two expressions for y equal to each other: 5x - 5 = -4x + 22, then solve for x.

Front

What is the solution to the system y = 5x - 5 and y = -4x + 22?

Back

The solution is (3, 10).