Math Problem Statement
Solution
The problem provided is in Indonesian, and it can be translated as:
"A line with the equation passes through the points and . The values of and , respectively, are . . ."
Steps to solve:
We are given the general form of the line equation and two points: and . We need to find the values of and .
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Substitute the points into the equation:
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For the point : a(3) + b(-2) = 8 \implies 3a - 2b = 8 \tag{1}
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For the point : a(2) + b(4) = 8 \implies 2a + 4b = 8 \tag{2}
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Solve the system of equations:
From equation (1):
From equation (2):
Now, we can solve these two simultaneous equations to find and .
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Multiply equation (2) by 2 to match the coefficient of with that in equation (1): 4a + 8b = 16 \tag{3}
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Subtract equation (1) from equation (3): Simplifying: a + 10b = 8 \tag{4}
- Solve for and :
Now, from equation (4):
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Rearrange:
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Substitute this into equation (2): Simplifying:
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Substitute into :
Final Answer:
The values of and are and , respectively.
Would you like more details on the solution process or have any other questions?
Here are 5 related questions to consider:
- How do you solve a system of linear equations using substitution?
- Can you find the equation of the line in slope-intercept form from the two points given?
- How does the standard form of a line equation relate to its slope and intercept?
- How can you verify that the points and satisfy the final equation ?
- What are other methods to solve systems of equations, such as elimination?
Tip: Always double-check by substituting the values back into the original equations to confirm the solution is correct.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Simultaneous equations
Formulas
ax + by = c
Substitution method
System of linear equations
Theorems
System of equations can be solved by substitution or elimination methods.
Suitable Grade Level
Grades 9-10
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