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Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0?
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Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=...
**Solution for 2x + y - 6 = 0:**
To find the solutions for this equation, we will use two methods - graphical method and substitution method.
**Graphical Method:**
1. Plot the graph of the equation by assigning different values to x and finding the corresponding y values.
2. Let's choose three different values for x: -2, 0, and 2.
- For x = -2, substitute in the equation: 2(-2) + y - 6 = 0, which gives y = 10.
- For x = 0, substitute in the equation: 2(0) + y - 6 = 0, which gives y = 6.
- For x = 2, substitute in the equation: 2(2) + y - 6 = 0, which gives y = 2.
3. Plot the points (-2, 10), (0, 6), and (2, 2) on the graph.
4. Draw a straight line passing through these points.
5. The solutions to the equation are the points where the line intersects the x-axis.
6. In this case, the line intersects the x-axis at the point (3, 0).
7. Therefore, the solutions to the equation 2x + y - 6 = 0 are x = 3.
**Substitution Method:**
1. Solve one of the equations for one variable in terms of the other variable.
2. Let's solve the equation 2x + y - 6 = 0 for y.
- Rearrange the equation: y = 6 - 2x.
3. Substitute this expression into the other equation.
- Substitute y = 6 - 2x into the equation x - 3y + 8 = 0.
- Simplify the equation: x - 3(6 - 2x) + 8 = 0.
- Expand and solve for x: x - 18 + 6x + 8 = 0.
- Combine like terms: 7x - 10 = 0.
- Solve for x: 7x = 10, x = 10/7.
4. Substitute the value of x into the first equation to find y.
- Substitute x = 10/7 into the equation 2x + y - 6 = 0.
- Simplify the equation: 2(10/7) + y - 6 = 0.
- Solve for y: y = 6 - 20/7 = 42/7 - 20/7 = 22/7.
5. Therefore, the solutions to the equation 2x + y - 6 = 0 are x = 10/7 and y = 22/7.
**Solution for x - 3y + 8 = 0:**
To find the solutions for this equation, we will use two methods - graphical method and substitution method.
**Graphical Method:**
1. Plot the graph of the equation by assigning different values to x and finding the corresponding y values.
2. Let's choose three different values for x: -2, 0, and 2.
- For x = -2, substitute in the equation: (-2) -
To find the solutions for this equation, we will use two methods - graphical method and substitution method.
**Graphical Method:**
1. Plot the graph of the equation by assigning different values to x and finding the corresponding y values.
2. Let's choose three different values for x: -2, 0, and 2.
- For x = -2, substitute in the equation: 2(-2) + y - 6 = 0, which gives y = 10.
- For x = 0, substitute in the equation: 2(0) + y - 6 = 0, which gives y = 6.
- For x = 2, substitute in the equation: 2(2) + y - 6 = 0, which gives y = 2.
3. Plot the points (-2, 10), (0, 6), and (2, 2) on the graph.
4. Draw a straight line passing through these points.
5. The solutions to the equation are the points where the line intersects the x-axis.
6. In this case, the line intersects the x-axis at the point (3, 0).
7. Therefore, the solutions to the equation 2x + y - 6 = 0 are x = 3.
**Substitution Method:**
1. Solve one of the equations for one variable in terms of the other variable.
2. Let's solve the equation 2x + y - 6 = 0 for y.
- Rearrange the equation: y = 6 - 2x.
3. Substitute this expression into the other equation.
- Substitute y = 6 - 2x into the equation x - 3y + 8 = 0.
- Simplify the equation: x - 3(6 - 2x) + 8 = 0.
- Expand and solve for x: x - 18 + 6x + 8 = 0.
- Combine like terms: 7x - 10 = 0.
- Solve for x: 7x = 10, x = 10/7.
4. Substitute the value of x into the first equation to find y.
- Substitute x = 10/7 into the equation 2x + y - 6 = 0.
- Simplify the equation: 2(10/7) + y - 6 = 0.
- Solve for y: y = 6 - 20/7 = 42/7 - 20/7 = 22/7.
5. Therefore, the solutions to the equation 2x + y - 6 = 0 are x = 10/7 and y = 22/7.
**Solution for x - 3y + 8 = 0:**
To find the solutions for this equation, we will use two methods - graphical method and substitution method.
**Graphical Method:**
1. Plot the graph of the equation by assigning different values to x and finding the corresponding y values.
2. Let's choose three different values for x: -2, 0, and 2.
- For x = -2, substitute in the equation: (-2) -
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Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0?
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Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0?.
Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Write 3 solutions for each of the following equations 2x y 6=0 x-3y 8=0 2x 3y-12=0?.
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