Substitution System of Equations

Front

What is a 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.

Front

How do you solve for y in the equation y = -6x + 5?

Back

To solve for y, simply substitute any value of x into the equation.

Front

What does it mean if two equations have no solution?

Back

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

Front

What is the solution to the system of equations: 2x + y = 5 and y = 2x - 11?

Back

The solution is (4, -3).

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 they hold true.

Front

What is the first step in using the substitution method?

Back

Isolate one variable in one of the equations.

Front

What does the solution (1, 3) represent in a system of equations?

Back

It represents the point where the two lines intersect on a graph.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line on a graph.

Front

What does it mean if two equations are dependent?

Back

It means they represent the same line, resulting in infinitely many solutions.

Front

How do you find the x-intercept of the equation y = -3x + 11?

Back

Set y to 0 and solve for x: 0 = -3x + 11, so x = 11/3.