Substitution Method Skill Check

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in using the substitution method?

Back

Identify one equation and solve for one variable in terms of the other variable.

Front

Given the equations x = 7 - 2y and 2x + y = 5, what is the first step?

Back

Substitute x in the second equation: 2(7 - 2y) + y = 5.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

In the equation 0 = 0, what type of solution does it represent?

Back

It represents infinite solutions, as any value for the variable will satisfy the equation.

Front

In the equation -5 = 52, what type of solution does it represent?

Back

It represents no solution, as the equation is false.

Front

How do you solve for y in the equation y = -1x - 5?

Back

You can substitute this expression for y into another equation to find the value of x.

Front

What is the second step in solving the system x = 7 - 2y and 2x + y = 5?

Back

Substituting x into the second equation gives: 14 - 4y + y = 5.

Front

What is the result of substituting y = -1x - 5 into the equation 4x - 8y = 4?

Back

The result is 4x - 8(-1x - 5) = 4.