ALG Systems of Equations - Substitution - Word Problems

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 does substitution mean in the context of solving equations?

Back

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you write an equation from a word problem?

Back

Identify the variables, translate the relationships and conditions into mathematical expressions, and then combine them into an equation.

Front

What is the first step in solving a system of equations using substitution?

Back

Isolate one variable in one of the equations.

Front

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

Back

y = 2(4) + 3 = 8 + 3 = 11.

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

How can you check if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations. If both equations are true, the point is a solution.

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

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

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

Front

What is the meaning of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.