(3) Unit 6: Systems of Equations - Writing Equations & Solving

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

How do you write an equation from a word problem?

Back

Identify the variables, translate the relationships described in the problem into mathematical expressions, and set them equal to the totals given.

Front

What does 'x' typically represent in a system of equations?

Back

In a system of equations, 'x' usually represents one of the unknown quantities we are trying to solve for.

Front

What does 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' usually represents the other unknown quantity we are trying to solve for.

Front

How can you solve a system of equations graphically?

Back

By graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What is the substitution method for 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

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the meaning of 'slope' in a linear equation?

Back

The slope is a measure of how steep a line is, calculated as the rise over run between two points on the line.

Front

What is the y-intercept in a linear equation?

Back

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