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Consider this system of equations:
[tex]\[
\begin{array}{l}
x + 2y = 5 \\
-x + 3y = 6
\end{array}
\][/tex]

The [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-intercepts of the first equation are found below:

[tex]\( x \)[/tex]-intercept:
[tex]\[
\begin{array}{l}
x + 2(0) = 5 \\
x = 5 \\
(5,0)
\end{array}
\][/tex]

[tex]\( y \)[/tex]-intercept:
[tex]\[
\begin{array}{l}
0 + 2y = 5 \\
2y = 5 \\
y = \frac{5}{2} = 2.5 \\
(0, 2.5)
\end{array}
\][/tex]

Find the intercepts for the equation [tex]\(-x + 3y = 6\)[/tex]:

What is the [tex]\( x \)[/tex]-intercept?
[tex]\[ \boxed{(?,0)} \][/tex]

What is the [tex]\( y \)[/tex]-intercept?
[tex]\[ \boxed{(0,?)} \][/tex]



Answer :

GinnyAnswer
To find the intercepts for the equation [tex]\(-x + 3y = 6\)[/tex], follow these steps:

### Finding the [tex]\(x\)[/tex]-intercept:
To find the [tex]\(x\)[/tex]-intercept, set [tex]\(y = 0\)[/tex] and solve for [tex]\(x\)[/tex].

1. Substitute [tex]\(y = 0\)[/tex] in the equation [tex]\(-x + 3y = 6\)[/tex]:
[tex]\[ -x + 3(0) = 6 \][/tex]
2. Simplify the equation:
[tex]\[ -x = 6 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -6 \][/tex]

So, the [tex]\(x\)[/tex]-intercept is [tex]\((-6, 0)\)[/tex].

### Finding the [tex]\(y\)[/tex]-intercept:
To find the [tex]\(y\)[/tex]-intercept, set [tex]\(x = 0\)[/tex] and solve for [tex]\(y\)[/tex].

1. Substitute [tex]\(x = 0\)[/tex] in the equation [tex]\(-x + 3y = 6\)[/tex]:
[tex]\[ -0 + 3y = 6 \][/tex]
2. Simplify the equation:
[tex]\[ 3y = 6 \][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{6}{3} = 2 \][/tex]

So, the [tex]\(y\)[/tex]-intercept is [tex]\((0, 2)\)[/tex].

In summary:
- The [tex]\(x\)[/tex]-intercept is [tex]\((-6, 0)\)[/tex]
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, 2)\)[/tex]

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