Question
Write rach equation in standard form using intergers. \( \begin{array}{ll}25 .) y+5=-(x+3) & 26 .) y-1=-\frac{1}{2}(x-4)\end{array} \)
Ask by Stephens Gray. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equations in standard form are:
1. \( x + y = -8 \)
2. \( x + 2y = 6 \)
Solution
1. For the equation
\[
y + 5 = -(x + 3)
\]
first expand the right-hand side:
\[
y + 5 = -x - 3.
\]
Next, add \(x\) to both sides:
\[
x + y + 5 = -3.
\]
Then, subtract \(5\) from both sides:
\[
x + y = -8.
\]
The equation in standard form is:
\[
x + y = -8.
\]
2. For the equation
\[
y - 1 = -\frac{1}{2}(x - 4),
\]
multiply both sides by \(2\) to eliminate the fraction:
\[
2(y - 1) = -(x - 4).
\]
Expanding both sides gives:
\[
2y - 2 = -x + 4.
\]
Add \(x\) to both sides:
\[
x + 2y - 2 = 4.
\]
Finally, add \(2\) to both sides:
\[
x + 2y = 6.
\]
The equation in standard form is:
\[
x + 2y = 6.
\]
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Simplify this solution The Deep Dive
To rewrite each equation in standard form using integers, we need to rearrange them into the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers. For the first equation, \(y + 5 = -(x + 3)\): 1. Distribute the negative: \(y + 5 = -x - 3\) 2. Rearrange to get standard form: \(x + y = -8\) So, the standard form is \(x + y = -8\). For the second equation, \(y - 1 = -\frac{1}{2}(x - 4)\): 1. Distribute \(-\frac{1}{2}\): \(y - 1 = -\frac{1}{2}x + 2\) 2. Rearrange to express \(y\): \(y = -\frac{1}{2}x + 3\) 3. Multiply the entire equation by 2 to eliminate the fraction: \(2y = -x + 6\) 4. Rearranging gives: \(x + 2y = 6\) So, the standard form is \(x + 2y = 6\).
