Question

Consider this system of equations.
 x + 2y = 5,
 –x + 3y = 6

The x- and y-intercepts of the first equation are found below.

x-intercept:

y-intercept:

x + 2(0) = 5
x = 5

(5, 0)

(0) + 2y = 5
2y = 5

y = 5
2
= 2.5

Find the intercepts for the equation –x + 3y = 6.

What is the x-intercept?


What is the y-intercept?

Answer 1

To find the intercepts for the equation \(-x + 3y = 6\), we will calculate both the x-intercept and y-intercept.

**1. Finding the x-intercept:**
To find the x-intercept, set \(y = 0\) and solve for \(x\):

\[
-x + 3(0) = 6
\]
\[
-x = 6
\]
\[
x = -6
\]

So the x-intercept is \((-6, 0)\).

**2. Finding the y-intercept:**
To find the y-intercept, set \(x = 0\) and solve for \(y\):

\[
-(0) + 3y = 6
\]
\[
3y = 6
\]
\[
y = \frac{6}{3} = 2
\]

So the y-intercept is \((0, 2)\).

**Summary:**
- The x-intercept is \((-6, 0)\).
- The y-intercept is \((0, 2)\).