### Solve the System of Equations by GraphingConsider the following system of linear equations:\[\begin{cases} y = -2x + 2 \\y = \frac{1}{2}x - 3 \end{cases}\]To graphically solve this system, we plot each equation on the coordinate grid.1. **Graph of \( y = -2x + 2 \):** - **Y-Intercept:** When \( x = 0 \), \( y = 2 \). So, the point (0, 2) is on the line. - **Slope:** The slope is -2, which means for every 1 unit increase in \( x \), \( y \) decreases by 2 units. 2. **Graph of \( y = \frac{1}{2}x - 3 \):** - **Y-Intercept:** When \( x = 0 \), \( y = -3 \). So, the point (0, -3) is on the line. - **Slope:** The slope is \(\frac{1}{2}\), which means for every 2 units increase in \( x \), \( y \) increases by 1 unit.### Graph InterpretationThe provided coordinate grid ranges from -6 to 6 on both the x-axis and y-axis. - **Steps to Plot \( y = -2x + 2 \):** - Start at the y-intercept (0, 2). - Use the slope to find another point. For example, moving one unit to the right (x = 1) gives you \( y = -2(1) + 2 = 0 \). Plot the point (1, 0). - Connect these points with a straight line.- **Steps to Plot \( y = \frac{1}{2}x - 3 \):** - Start at the y-intercept (0, -3). - Use the slope to find another point. For example, moving two units to the right (x = 2) gives you \( y = \frac{1}{2}(2) - 3 = -2 \). Plot the point (2, -2). - Connect these points with a straight line.### Intersection PointThe intersection point of the two lines represents the solution to the system of

Answered: Image /qna-images/answer/e8c6c111-24dd-410b-b746-341a7b69878b.jpg

Answered: Solve the system of equations by…

Math

Algebra

Solve the system of equations by graphing: -2x + 2 Sy= โy = 1x - 3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: solve the system using subsitution -x +3y=15 2x+3y+60

Q: Solve each system 5x+2y=-13 -3x+y=10

A: Let Multiply equation 1 with "3" and equation 2 with 5 and add them both.

Q: Solve the system: 4x2 + y2 = 13, x2 + y2 = 10.

A: we have to solve the system of equations: 4x2+y2=13x2+y2=10

Q: Solve the system +4x3 -6 X1 -x2 -6 +7x3 +27x3 5x1 -4x2 -3x1 -54 +s

A: We have the following system of equations - x1-x2+4x3 = -65x1-4x2+7x3 = -6-3x1+27x3 = -54

Q: How many solutions in this system of equations? y=3x-5 6x-2y=10

Q: Solve the system -a+4b+2c=-8 3a+b-4c=9 b=-1

Q: -2x-2y =-8 3x+6y 21

Q: One piece of chocolate 3 grams of sugar, and one piece of starburst candy contains 5 grams of sugar.…

A: Let the number of chocolate pieces in the bag be x. To find the total amount of sugar in x…

Q: The developers of a web site are tracking its number of adult users and teenage users. They found…

A: Given that: 82x+y=695 ..........(1)127x-2y=-128 ..........)2(

Q: The distance, d, that a certain car is from Math City after h hours, can be determined by the…

A: Given, The distance, d, that a certain car is from Math City after h hours, can be…

Question

### Solve the System of Equations by Graphing

Consider the following system of linear equations:

\[
\begin{cases}
y = -2x + 2 \\
y = \frac{1}{2}x - 3
\end{cases}
\]

To graphically solve this system, we plot each equation on the coordinate grid.

1. **Graph of \( y = -2x + 2 \):**
- **Y-Intercept:** When \( x = 0 \), \( y = 2 \). So, the point (0, 2) is on the line.
- **Slope:** The slope is -2, which means for every 1 unit increase in \( x \), \( y \) decreases by 2 units.

2. **Graph of \( y = \frac{1}{2}x - 3 \):**
- **Y-Intercept:** When \( x = 0 \), \( y = -3 \). So, the point (0, -3) is on the line.
- **Slope:** The slope is \(\frac{1}{2}\), which means for every 2 units increase in \( x \), \( y \) increases by 1 unit.

### Graph Interpretation

The provided coordinate grid ranges from -6 to 6 on both the x-axis and y-axis.

- **Steps to Plot \( y = -2x + 2 \):**
- Start at the y-intercept (0, 2).
- Use the slope to find another point. For example, moving one unit to the right (x = 1) gives you \( y = -2(1) + 2 = 0 \). Plot the point (1, 0).
- Connect these points with a straight line.

- **Steps to Plot \( y = \frac{1}{2}x - 3 \):**
- Start at the y-intercept (0, -3).
- Use the slope to find another point. For example, moving two units to the right (x = 2) gives you \( y = \frac{1}{2}(2) - 3 = -2 \). Plot the point (2, -2).
- Connect these points with a straight line.

### Intersection Point

The intersection point of the two lines represents the solution to the system of

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Plotting the graph

VIEW

Step 3: Graph

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Solve each systems of equations by substitution
Solve the equation: V4x2 +1= 2x +2
solve the system using elimination 2x+3y=20 -3x+ 5y = 65
Solve each system
A group of volunteers worked to clean up a park over 2 days. The number of volunteers on the second day was 5 more than half of the number of volunteers on the first day. There were 21 volunteers the second day. Write an equation to find the number of volunteers, v, on the first day.
In a cliff diving championship in Acapulco, a diver dives from a cliff. Write the equation that describes his height during the dive if in the beginning when t=0 sec he was 70 feet above the ocean, after 1 sec he was 74 feet above the ocean, and after 2 sec he was 46 feet above the ocean.Write the system on equations
A rectangular swimming pool is x meters wide. The length of the swimming pool is twice as long as the width. If the perimeter of the pool is 64 meters, what is the solution
solve system of equations by graphing two lines 24x-27y=243 y= -7/9x +6
Solve the system: 3x+2y ≡ 5mod17 2x+7y ≡ 9mod17
Solve the system using any method. Зх- 4y %3D700 2y+ 300 = x
Solve the system of equations using elimination -x +y = -4 -5x + 7y = -14