Answer :
Final answer:
To solve the system of equations using linear combination, multiply the equations by different numbers to eliminate a variable. Add the resulting equations to eliminate the x variable. Solve for y and substitute it back into one of the original equations to solve for x. The solution to the system of equations is x = 15 and y = 9.
Explanation:
To solve the system of equations using linear combination, we can eliminate one variable by multiplying one or both equations by different numbers so that the coefficients of one variable are the same in both equations.
In this case, we can multiply the first equation by 3.5 and the second equation by -1 to eliminate the x variable.
Multiplying the first equation by 3.5 gives us 3.5x + 3.5y = 84. Multiplying the second equation by -1 gives us -3.5x - 5y = -97.5.
Now we can add these two equations together to eliminate the x variable. (3.5x - 3.5x) + (3.5y - 5y) = 84 - 97.5. This simplifies to -1.5y = -13.5.
Dividing both sides of the equation by -1.5 gives us y = 9. Substituting this value back into one of the original equations, we can solve for x. Using the first equation, we have x + 9 = 24. Subtracting 9 from both sides gives us x = 15.
Therefore, the solution to the system of equations is x = 15 and y = 9.
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