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Answer :
To solve the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex], we need to find the point where the two lines intersect. Here’s a step-by-step guide on how to do that:
1. Set up the equation:
We start with the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex].
2. Move the terms involving [tex]\(x\)[/tex] to one side:
[tex]\[
-\frac{1}{2}x - x = 1 - 4
\][/tex]
3. Combine like terms:
[tex]\[
-\frac{3}{2}x = -3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides by [tex]\(-\frac{3}{2}\)[/tex]:
[tex]\[
x = \frac{-3}{-\frac{3}{2}}
\][/tex]
Which simplifies to:
[tex]\[
x = 2
\][/tex]
5. Substitute [tex]\(x = 2\)[/tex] back into one of the original equations to find [tex]\(y\)[/tex]:
You can use either [tex]\(y = -\frac{1}{2}x + 4\)[/tex] or [tex]\(y = x + 1\)[/tex]. Let's use [tex]\(y = x + 1\)[/tex].
Substitute [tex]\(x = 2\)[/tex]:
[tex]\[
y = 2 + 1 = 3
\][/tex]
6. Conclusion:
The solution, or the point of intersection, is [tex]\((x, y) = (2, 3)\)[/tex].
Therefore, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]. The lines intersect at the point [tex]\((2, 3)\)[/tex].
1. Set up the equation:
We start with the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex].
2. Move the terms involving [tex]\(x\)[/tex] to one side:
[tex]\[
-\frac{1}{2}x - x = 1 - 4
\][/tex]
3. Combine like terms:
[tex]\[
-\frac{3}{2}x = -3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides by [tex]\(-\frac{3}{2}\)[/tex]:
[tex]\[
x = \frac{-3}{-\frac{3}{2}}
\][/tex]
Which simplifies to:
[tex]\[
x = 2
\][/tex]
5. Substitute [tex]\(x = 2\)[/tex] back into one of the original equations to find [tex]\(y\)[/tex]:
You can use either [tex]\(y = -\frac{1}{2}x + 4\)[/tex] or [tex]\(y = x + 1\)[/tex]. Let's use [tex]\(y = x + 1\)[/tex].
Substitute [tex]\(x = 2\)[/tex]:
[tex]\[
y = 2 + 1 = 3
\][/tex]
6. Conclusion:
The solution, or the point of intersection, is [tex]\((x, y) = (2, 3)\)[/tex].
Therefore, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]. The lines intersect at the point [tex]\((2, 3)\)[/tex].
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