Substitution Method

Front

What is the substitution method in solving systems of equations?

Back

The substitution method is a technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you solve for y in the equation y = -4x + 5?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = -4(1) + 5 = 1.

Front

What does it mean for two equations to intersect on a graph?

Back

It means that the two equations have a common solution, which is the point (x, y) where the graphs of the equations meet.

Front

If y = 3x - 16, what is y when x = 5?

Back

Substituting x = 5 into the equation gives y = 3(5) - 16 = 15 - 16 = -1.

Front

What is the first step in using the substitution method?

Back

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

Front

Given the equations y = -6 and -3x - 6y = 24, how do you find the solution?

Back

Substitute y = -6 into the second equation: -3x - 6(-6) = 24, which simplifies to -3x + 36 = 24, then solve for x.

Front

What is the solution to the system of equations y = -4x + 5 and y = 3x - 16?

Back

The solution is (3, -7), found by setting -4x + 5 = 3x - 16 and solving for x.

Front

What does the term 'system of equations' refer to?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

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

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

What is the significance of the point (1, -1) in a system of equations?

Back

It represents the solution where the two equations intersect, meaning both equations are true at that point.