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

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

Back

It means that the two equations have a common solution, represented by the point where their graphs meet.

Front

How do you determine which equation to solve for a variable in the substitution method?

Back

Choose the equation that is easiest to manipulate, typically the one with a coefficient of 1 or -1 for the variable you want to isolate.

Front

If y = 2x + 3, what is the new equation after substituting y into the equation 3x - 2y = 6?

Back

3x - 2(2x + 3) = 6.

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

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

Back

(1, 3).

Front

In the equation 2x + 3y = 12, what is y when x = 0?

Back

y = 4.

Front

What is the purpose of the substitution method?

Back

To find the values of the variables that satisfy both equations in a system.

Front

If you have the equations y = x + 2 and 2x + y = 10, what is the value of x?

Back

x = 2.

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.