Solve 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

If you have the equations x + 2y = 2 and x = -4y + 2, how do you solve for y?

Back

Substitute x = -4y + 2 into the first equation and solve for y.

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 do you determine if two lines are parallel?

Back

If their slopes are equal and their y-intercepts are different.

Front

Solve the system by substitution: y = 2x - 11 and -3y = -6x - 15.

Back

No solution (parallel lines).

Front

What is the substitution method used for?

Back

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

Front

Given the equations 5x + 4y = -14 and y = -7x - 15, what is the solution?

Back

(-2, -1).