Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter5: Solving Systems Of Linear Equations
Section: Chapter Questions
Problem 4CA
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Question
![### Finding the Intersection Point of Two Lines
To find the point at which the lines \( f(x) = -5x + 17 \) and \( g(x) = -3x + 9 \) intersect, follow these steps:
1. **Set the equations equal to each other:**
\[
-5x + 17 = -3x + 9
\]
2. **Solve for \( x \):**
\[
-5x + 17 = -3x + 9
\]
Add \( 3x \) to both sides:
\[
-5x + 3x + 17 = 9
\]
Combine like terms:
\[
-2x + 17 = 9
\]
Subtract 17 from both sides:
\[
-2x = 9 - 17
\]
Simplify:
\[
-2x = -8
\]
Divide by -2:
\[
x = 4
\]
3. **Substitute \( x \) back into one of the original equations to find \( y \):**
Use \( f(x) = -5x + 17 \):
\[
f(4) = -5(4) + 17
\]
Calculate:
\[
f(4) = -20 + 17 = -3
\]
Therefore, the lines intersect at the point \( (4, -3) \).
### Summary
The point at which the line \( f(x) = -5x + 17 \) intersects the line \( g(x) = -3x + 9 \) is:
\[
(4, -3)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48cff491-b173-4746-bb53-6890caeb4c28%2F00437344-b537-4d25-9eda-8de93bb7a73d%2Fvjl48u.png&w=3840&q=75)
Transcribed Image Text:### Finding the Intersection Point of Two Lines
To find the point at which the lines \( f(x) = -5x + 17 \) and \( g(x) = -3x + 9 \) intersect, follow these steps:
1. **Set the equations equal to each other:**
\[
-5x + 17 = -3x + 9
\]
2. **Solve for \( x \):**
\[
-5x + 17 = -3x + 9
\]
Add \( 3x \) to both sides:
\[
-5x + 3x + 17 = 9
\]
Combine like terms:
\[
-2x + 17 = 9
\]
Subtract 17 from both sides:
\[
-2x = 9 - 17
\]
Simplify:
\[
-2x = -8
\]
Divide by -2:
\[
x = 4
\]
3. **Substitute \( x \) back into one of the original equations to find \( y \):**
Use \( f(x) = -5x + 17 \):
\[
f(4) = -5(4) + 17
\]
Calculate:
\[
f(4) = -20 + 17 = -3
\]
Therefore, the lines intersect at the point \( (4, -3) \).
### Summary
The point at which the line \( f(x) = -5x + 17 \) intersects the line \( g(x) = -3x + 9 \) is:
\[
(4, -3)
\]
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