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.

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 first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If y = 2x + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 11.

Front

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

Back

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

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

Front

Solve the system by substitution: y = 3x + 1, 2x + y = 11.

Back

(3, 10).

Front

Solve the system by substitution: y = -x + 4, 3x + 2y = 6.

Back

(0, 4).

Front

What is the substitution method used for?

Back

To find the values of variables that satisfy all equations in the system.

Front

If you have the equations y = 2x + 1 and y = -x + 5, how do you find the solution?

Back

Set 2x + 1 = -x + 5 and solve for x.