Systems of Equations--Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation.

Front

What does it mean to solve for y in terms of x?

Back

It means to express y as a function of x, typically in the form y = mx + b.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

If y = 2x + 3, what is y when x = 4?

Back

Substituting x = 4 gives y = 2(4) + 3 = 8 + 3 = 11.

Front

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

Back

The solution is (1, 3), found by substituting y from the first equation into the second.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means there is no solution to the system, as they never intersect.