7.2 Substitutions

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you solve for y in the equation y = 2x?

Back

To solve for y, simply multiply the value of x by 2.

Front

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

Back

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

Front

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

Back

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

Front

Solve the system by substitution: -5x - 4y = -9, y = 6.

Back

(-3, 6)

Front

Solve the system by substitution: y = 2x, x + y = 9.

Back

(3, 6)

Front

Solve the system by substitution: 3x - y = -8, x = -2.

Back

(-2, 2)

Front

Solve the system by substitution: 7x - 10y = -23, x = -9.

Back

(-9, -4)

Front

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

Back

Isolate one variable in one of the equations.

Front

When substituting, what do you do with the isolated variable?

Back

Replace the isolated variable in the other equation with its expression.