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 the system: y = -2x + 18 and y = 8?

Back

Set -2x + 18 equal to 8 to find the value of x.

Front

What is the solution to the system: y = -2x + 18 and y = 8?

Back

(5, 8)

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 is the solution to the system: 3x + y = 1 and y = 4x + 1?

Back

(0, 1)

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines indicate that there is no point of intersection, hence no solution.

Front

What is the solution to the system: y = 2x - 11 and -3y = -6x - 15?

Back

No solution (parallel lines).

Front

What is the method to find the intersection of two lines represented by equations?

Back

Set the equations equal to each other and solve for the variable.

Front

What is the solution to the system: 7x + y = -20 and y = 3x + 10?

Back

(-3, 1)