Solving with Substitution - Practice

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 another equation to find the values of the variables.

Front

How do you solve for y in the equation y = -3x + 9?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 0, then y = 9.

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 infinitely many solutions?

Back

It means that the equations represent the same line, and there are an infinite number of points that satisfy both equations.

Front

Solve the system using substitution: y = 6x - 5 and 6x - 7y = -1.

Back

(1, 1)

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

Solve the system using substitution: y = 3 - x and 3y + x = 5.

Back

(2, 1)

Front

What is the solution to the system 2x + 3y = 4 and y = 5x - 27?

Back

(5, -2)

Front

How do you check if your solution to a system of equations is correct?

Back

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

Front

Solve with substitution: x = -3y - 8 and x - 2y = -3.

Back

(-5, -1)