Unit 6.5 Flashcardizz - Substitution Method

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you start solving a system of equations using the substitution method?

Back

Begin by isolating one variable in one of the equations, then substitute that expression into the other equation.

Front

What is the first step in solving the system of equations: 2x + 3y = 6 and x - y = 1 using substitution?

Back

Isolate x in the second equation: x = y + 1.

Front

After substituting x = y + 1 into the equation 2x + 3y = 6, what is the next step?

Back

Replace x in the first equation with (y + 1) to get 2(y + 1) + 3y = 6.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

The solution is (3, -2).

Front

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

Back

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

Front

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

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

How can you check your solution after using the substitution method?

Back

Substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Front

What is the solution to the system of equations: 3x + 4y = 5 and x - 2y = -1?

Back

The solution is (3, -4).

Front

What is the solution to the system of equations: x + 2y = 4 and 3x - y = 5?

Back

The solution is (-3, -2).