Solving Systems by Substitution

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 for y in the equation x = -3y - 17?

Back

To solve for y, rearrange the equation: y = (-x - 17)/3.

Front

What is the first step in using substitution to solve the system: 2y + x = -15 and x = 3y?

Back

The first step is to substitute the expression for x from the second equation (x = 3y) into the first equation.

Front

What does it mean if a system of equations has one solution?

Back

It means that the two lines represented by the equations intersect at exactly one point.

Front

How can you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

What is the solution to the system of equations y = x + 5 and 4x + y = 20?

Back

The solution is (3, 8).

Front

In the equation x = 7 - 2y, how can you express y in terms of x?

Back

Rearranging gives y = (7 - x)/2.

Front

What is the significance of the point (10, -9) in the context of the system x = -3y - 17 and 2x + 3y = -7?

Back

It is the solution to the system, meaning it satisfies both equations.

Front

What is the graphical representation of a system of equations with one solution?

Back

The graphical representation shows two lines intersecting at a single point.

Front

How do 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.