# Lesson 10

Solutions to Linear Equations

Let’s think about what it means to be a solution to a linear equation with two variables in it.

### Problem 1

Select all of the ordered pairs $$(x,y)$$ that are solutions to the linear equation $$2x+3y=6$$.

A:

$$(0,2)$$

B:

$$(0,6)$$

C:

$$(2,3)$$

D:

$$(3,\text-2)$$

E:

$$(3,0)$$

F:

$$(6,\text-2)$$

### Problem 2

The graph shows a linear relationship between $$x$$ and $$y$$.

$$x$$ represents the number of comic books Priya buys at the store, all at the same price, and $$y$$ represents the amount of money (in dollars) Priya has after buying the comic books.

1. Find and interpret the $$x$$- and $$y$$-intercepts of this line.

2. Find and interpret the slope of this line.

3. Find an equation for this line.
4. If Priya buys 3 comics, how much money will she have remaining?

### Problem 3

Match each equation with its three solutions.

### Problem 4

A container of fuel dispenses fuel at the rate of 5 gallons per second. If $$y$$ represents the amount of fuel remaining in the container, and $$x$$ represents the number of seconds that have passed since the fuel started dispensing, then $$x$$ and $$y$$ satisfy a linear relationship.

In the coordinate plane, will the slope of the line representing that relationship have a positive, negative, or zero slope? Explain how you know.

(From Unit 5, Lesson 9.)

### Problem 5

A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays$61 for 8 turkey sandwiches. How much does each turkey sandwich add to the cost of the delivery? Explain how you know.

(From Unit 5, Lesson 4.)