Solving Systems of Equations Using 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 using substitution?

Back

Solving a system of equations using 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, you perform 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 = 3 - x and 3y + x = 5?

Back

Substitute the expression for y from the first equation into the second equation.

Front

What is the solution to the system: -3x - 8y = 20 and -5x + y = 19?

Back

The solution is (-4, -1).

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

Back

The solution is (1, 9).

Front

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

Back

The solution is (6, 9).

Front

What is the solution to the system: y = 8 and y = -4x + 4?

Back

The solution is (-1, 8).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.