9.4 - Solving systems by substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

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

Back

Isolate one variable in one of the equations.

Front

Given the equations y = 2x + 3 and 3x + y = 12, how do you solve for x?

Back

Substitute y from the first equation into the second: 3x + (2x + 3) = 12.

Front

What is the solution to the system of equations 2x + y = 10 and y = 4x - 2?

Back

(2, 6) after substituting y into the first equation.

Front

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

Back

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

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How can you check your solution to a system of equations?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.

Front

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

Back

Set -x + 4 = 2x - 1 and solve for x.