The original number is 86
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Further explanation
Simultaneous Linear Equations could be solved by using several methods such as :
- Elimination Method
- Substitution Method
- Graph Method
If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.
Let us tackle the problem!
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Let:
The original number = yx
The ones digit = x
The tens digit = y
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The ones digit in it is 2 less than the tens digit.
[tex]\boxed {x = y - 2}[/tex] → Equation 1
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The sum of the reversed number and the original number is 154.
[tex]xy + yx = 154[/tex]
[tex](10x + y) + (10y + x) = 154[/tex]
[tex]11x + 11y = 154[/tex]
[tex]\boxed {x + y = 14}[/tex] → Equation 2
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Equation 1 ↔ Equation 2 :
[tex]x + y = 14[/tex]
[tex]( y - 2 ) + y = 14[/tex]
[tex]2y - 2 = 14[/tex]
[tex]2y = 14 + 2[/tex]
[tex]2y = 16[/tex]
[tex]y = 16 \div 2[/tex]
[tex]y = 8[/tex]
[tex]x = y - 2[/tex]
[tex]x = 8 - 2[/tex]
[tex]x = 6[/tex]
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Conclusion:
The original number is 86
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Learn more
- Perimeter of Rectangle : https://brainly.com/question/12826246
- Elimination Method : https://brainly.com/question/11233927
- Sum of The Ages : https://brainly.com/question/11240586
Answer details
Grade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations
