4.13-4.14 Solving Systems 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 = -1x - 5 and 4x - 8y = 4?

Back

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

Front

What is the solution to the system: y = 4x - 10 and y = 3x - 5?

Back

(5, 10)

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, they have no points of intersection, meaning the system has no solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations.

Front

What is the solution to the system: x = -3y - 17 and 2x + 3y = -7?

Back

(10, -9)

Front

What is the significance of the ordered pair in the context of systems of equations?

Back

The ordered pair represents the point where the two equations intersect, indicating the values of the variables that satisfy both equations.

Front

What is the solution to the system: y = 7x + 7 and 2y + 2x = -18?

Back

(-2, -7)