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If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
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Q1
If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
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From the second equation, x = 10 - 2y. Substituting into the first gives 2(10 - 2y) + 3y = 12, solving gives y = 2, x = 6.
Questions & Step-by-step Solutions
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Q
Q: If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
Solution:
From the second equation, x = 10 - 2y. Substituting into the first gives 2(10 - 2y) + 3y = 12, solving gives y = 2, x = 6.
Steps: 11
Show Steps
Step 1: Start with the two equations: 2x + 3y = 12 and x + 2y = 10.
Step 2: From the second equation (x + 2y = 10), we want to express x in terms of y. Rearranging gives us x = 10 - 2y.
Step 3: Now, we will substitute the expression for x (10 - 2y) into the first equation (2x + 3y = 12).
Step 4: Substitute: 2(10 - 2y) + 3y = 12.
Step 5: Simplify the left side: 20 - 4y + 3y = 12.
Step 6: Combine like terms: 20 - y = 12.
Step 7: To isolate y, subtract 20 from both sides: -y = 12 - 20.
Step 8: This simplifies to -y = -8, so y = 8.
Step 9: Now that we have y, we can find x. Substitute y = 2 back into the equation x = 10 - 2y.
Step 10: Substitute: x = 10 - 2(2).
Step 11: Simplify: x = 10 - 4, which gives x = 6.
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