Solving Systems of Equations by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

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

Back

Choose one equation and solve for one variable in terms of the other variable.

Front

Given the equations x = 7 - 2y and 2x + y = 5, what is the value of y when x = 1?

Back

y = 3.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection of the lines representing each equation on a coordinate plane.

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you find the solution?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.