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1. The solution
Look into the two equations. Their left sides are IDENTICAL, right ?
Hence, their right sides are equal:
3x - 7 = -x + 9
3x + x = 9 + 7
4x = 16 ====> x = = 4.
Then from the first equation y = 3x-7 = 3*4 - 7 = 12-7 = 5.
Answer. x= 4, y= 5.
2. Checking / (verifying)
Substitute the obtained values x= 5, y= 5 into the original equations.
a) First equation becomes 5 = 3*4 - 7. Is is true ? - YES, it is. Thus first equation is just checked.
b) Second equation becomes 5 = -4 + 9. Is it TRUE ? - YES, it is. Thus second equation is just checked, too.
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The check is completed.
The solution is completed.
You are done.