Substitution Method - Linear Systems

Front

What is the substitution method in solving linear systems?

Back

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

Front

What does it mean for two lines to intersect in a linear system?

Back

It means that there is a unique solution (x, y) that satisfies both equations.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

Front

What is the first step in using the substitution method?

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how would you solve using substitution?

Back

Substitute y from the first equation into the second: 4x - (2x + 3) = 1.

Front

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

Back

It means the lines are parallel and will never intersect.

Front

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

Back

(1, 4) is the solution.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the values of x and y that satisfy both equations.

Front

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

Back

Plug the solution back into both original equations to verify.