Final answer:
To solve the system of linear equations, the second equation is simplified to find y=3, which is substituted into the first equation to find x=1, resulting in a solution of x=1 and y=3.
Step-by-step explanation:
To solve the given linear equations with two unknowns, 21x+7y=42 and -5+5y=10, we can follow a step-by-step method. Let's start by simplifying and rewriting the equations if necessary, then use either substitution or elimination methods to find the values of x and y.
First, let's simplify the second equation:
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- -5 + 5y = 10
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- Add 5 to both sides to isolate the term with y: 5y = 15
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- Divide both sides by 5 to solve for y: y = 3
Having found that y = 3, we can substitute it into the first equation to find x:
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- 21x + 7(3) = 42
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- 21x + 21 = 42
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- Subtract 21 from both sides: 21x = 21
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- Divide both sides by 21: x = 1
Now we have the solution to the system of equations, which is x = 1 and y = 3.
It is important to note that linear equations are generally in the form y = a + bx, where 'a' is the y-intercept, 'b' is the slope, 'x' is the independent variable, and 'y' is the dependent variable. This form applies to a multitude of real-world situations, such as relating the number of flu cases to the year or determining the total cost based on the number of years enrolled in an institution.