Solving Systems: 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 does substitution mean in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted 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 is the first step in solving the system: y = 2x + 1 and y = 4x - 1?

Back

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

Front

What is the solution to the system y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3).

Front

How do you find the x-value in the system y = 5x + 1 and y = 3x + 13?

Back

Set the equations equal: 5x + 1 = 3x + 13, then solve for x.

Front

What is the solution to the system y = 5x + 1 and y = 3x + 13?

Back

The solution is (6, 31).

Front

What does it mean if two equations have no solution?

Back

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

Front

How do you solve the equation y = x - 2 and -2x + 3y = -1?

Back

Substitute y from the first equation into the second equation and solve for x.

Front

What is the solution to the system y = x - 2 and -2x + 3y = -1?

Back

The solution is (5, 3).