If x + 2y = 10 and 2x - y = 3, what is the value of x?

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Q: If x + 2y = 10 and 2x - y = 3, what is the value of x?

Solution: From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.

Steps: 11

Step 1: Start with the first equation: x + 2y = 10.
Step 2: Rearrange the first equation to solve for x: x = 10 - 2y.
Step 3: Now take the second equation: 2x - y = 3.
Step 4: Substitute the expression for x from Step 2 into the second equation: 2(10 - 2y) - y = 3.
Step 5: Simplify the equation: 20 - 4y - y = 3.
Step 6: Combine like terms: 20 - 5y = 3.
Step 7: Move 20 to the other side: -5y = 3 - 20.
Step 8: Simplify the right side: -5y = -17.
Step 9: Divide both sides by -5 to solve for y: y = 17/5 or y = 3.4.
Step 10: Now substitute y back into the expression for x: x = 10 - 2(3.4).
Step 11: Calculate: x = 10 - 6.8 = 3.2.