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Solve the system of equations x + 2y = 10 and 3x − y = 5, then calculate 2x - 2y.
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5 stepsYour method for solving the system of equations and calculating the expression is correct. However, rounding the intermediate values for and to two decimal places introduces a slight error in the final answer. It's generally best to keep values as fractions until the final step to maintain accuracy.
Let's re-evaluate using exact fractions:
Given the system of equations:
Solve for in terms of from equation (1).
Substitute this expression for into equation (2).
Solve for .
Substitute the exact value of back into the expression for .
To combine, find a common denominator:
Calculate the value of using the exact values of and .
As a decimal,
Rounding to two decimal places, the value is .Your final answer of is very close, but due to rounding to 3.57 and to 2.86 in intermediate steps, there's a slight difference.
The more accurate value is or approximately .
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