Substitution Method

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 solve for y in the equation y = 2x + 1?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = 2(1) + 1 = 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 will never intersect.

Front

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

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

Front

Solve the system using substitution: y = 3x - 8 and y = 4 - x. What is the solution?

Back

The solution is (3, 1).

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.

Front

If you have the equations y = 2x + 1 and y = 4x - 1, how do you find the solution?

Back

Set the two equations equal to each other: 2x + 1 = 4x - 1, then solve for x.

Front

What is the solution to the system of equations: x = -3y - 17 and 2x + 3y = -7?

Back

The solution is (10, -9).

Front

What is a key characteristic of a system of equations with exactly one solution?

Back

The lines intersect at exactly one point.

Front

How can 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.