Systems with Substitution Review

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 to find the values of both variables.

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 x = -3y - 8 and x - 2y = -3, solve for (x, y) using substitution.

Back

(-5, -1)

Front

What is the first step when using substitution with the equations 3x + 3y = 3 and y = 3x + 5?

Back

Substitute y in the first equation: 3x + 3(3x + 5) = 3.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and there are countless points of intersection.

Front

Solve the system of equations: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

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.

Front

Given the equations y = 3 - x and 3y + x = 5, solve for (x, y) using substitution.

Back

(2, 1)

Front

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

Back

The point of intersection represents the solution to the system, where both equations are satisfied.