5-3 Substitution Method

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you solve the equation -7x - 2y = -13 for y?

Back

To solve for y, rearrange the equation: 2y = -7x + 13, then y = (-7/2)x + 13/2.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

Given the equations y = 2x - 4 and 7x - 2y = 5, how do you use substitution to find the solution?

Back

Substitute y = 2x - 4 into the second equation: 7x - 2(2x - 4) = 5, then solve for x.

Front

What is the solution to the system of equations -7x - 2y = -13 and x = 2y + 11?

Back

The solution is (3, -4).

Front

How do you check if a solution (x, y) is correct for a system of equations?

Back

Substitute the values of x and y into both original equations. If both equations are satisfied, the solution is correct.

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 is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

How do you isolate x in the equation 6(x - 1) = 6?

Back

Distribute to get 6x - 6 = 6, then add 6 to both sides to get 6x = 12, and finally divide by 6 to find x = 2.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation shows the lines of the equations on a coordinate plane, where the intersection points represent the solutions.