(1) 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 into mathematical expressions, and set up the equation based on the given information.

Front

What does 'x' typically represent in a word problem involving sales?

Back

'x' usually represents the quantity of one type of item being sold.

Front

What does 'y' typically represent in a word problem involving sales?

Back

'y' usually represents the quantity of another type of item being sold.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Front

What is the cost of an item if the equation is 4x + 8y = 80 and x = 5?

Back

Substituting x = 5 into the equation gives 4(5) + 8y = 80, which simplifies to 8y = 60, so y = 7.5.

Front

If Emma sold 4 boxes of cookies and 8 brownies for $80, how can you express this as an equation?

Back

The equation is 4x + 8y = 80, where x is the price of cookies and y is the price of brownies.

Front

What is the first step in solving the equations 3x + 9y = 75 and 8x + 5y = 67?

Back

You can use either substitution or elimination. Choose one method to start solving.

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.