Solving Systems of Equations by 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 equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another 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 = 3, then y = 2(3) + 1 = 7.

Front

What is the first step in solving a system of equations by substitution?

Back

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

Front

Given the equations 5x - 2y = 3 and y = 2x, how do you substitute?

Back

Substitute y = 2x into the first equation: 5x - 2(2x) = 3.

Front

What is the solution to the system 2x + 3y = 4 and y = 5x - 27?

Back

The solution is (5, -2).

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations. If both equations are true, the solution is correct.

Front

What does it mean if two lines represented by a system of equations intersect at one point?

Back

It means the system has a unique solution, which is the point of intersection.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation is two parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The graphical representation is two lines that overlap completely, meaning they are the same line.