Solving systems of equations by substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the first step in solving the system: y = 2x + 1 and y = 4x - 1?

Back

Substitute the expression for y from the first equation into the second equation: 2x + 1 = 4x - 1.

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3).

Front

What is the solution to the system: y = 8x + 1 and y = 6x + 3?

Back

The solution is (1, 9).

Front

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

Back

A system has no solution if 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

A system has infinite solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

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

Back

Substitute the solution back into both original equations to see if it satisfies both.

Front

What is the solution to the system: y = -6x + 5 and -2x + y = 5?

Back

The solution is (0, 5).