document.write( "Question 175233: i cant figure out how to get \"X\" and \"Y\"...\r
\n" ); document.write( "\n" ); document.write( "4x + 6y = 38
\n" ); document.write( "10x + 8Y = 60\r
\n" ); document.write( "\n" ); document.write( "they have steps but i dont understand them, please help \n" ); document.write( "
Algebra.Com's Answer #130307 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
you have 2 equations in 2 unknowns.
\n" ); document.write( "you need to eliminate one of the unknowns so you can solve for the remaining one.
\n" ); document.write( "you do this by manipulating the equations so that when you add or subtract one equation from the other, the second unknown disappears.
\n" ); document.write( "---
\n" ); document.write( "here's how it's done.
\n" ); document.write( "your equations are:
\n" ); document.write( "4x + 6y = 38
\n" ); document.write( "10x + 8y = 60
\n" ); document.write( "---
\n" ); document.write( "if you multiply the first equation by 10, and you multiply the second equation by 4, you will be able to eliminate the x as follows:
\n" ); document.write( "---
\n" ); document.write( "first equation:
\n" ); document.write( "4x + 6y = 38
\n" ); document.write( "multiply both sides of the equation by 10 to get:
\n" ); document.write( "40x + 60y = 380
\n" ); document.write( "---
\n" ); document.write( "second equation:
\n" ); document.write( "10x + 8y = 60
\n" ); document.write( "multiply both sides of the equation by 4 to get:
\n" ); document.write( "40x + 32y = 240
\n" ); document.write( "---
\n" ); document.write( "your two equations are now:
\n" ); document.write( "40x + 60y = 380
\n" ); document.write( "40x + 32y = 240
\n" ); document.write( "---
\n" ); document.write( "subtract the second equation from the first to get:
\n" ); document.write( "0x + 28y = 140
\n" ); document.write( "which becomes:
\n" ); document.write( "28y = 140
\n" ); document.write( "divide both sides of this equation by 28 to get:
\n" ); document.write( "y = 5
\n" ); document.write( "---
\n" ); document.write( "now that you have solved for y, you can substitute in either equation to find x.
\n" ); document.write( "go back to your original equations:
\n" ); document.write( "4x + 6y = 38
\n" ); document.write( "10x + 8y = 60
\n" ); document.write( "---
\n" ); document.write( "take the second equation and substitute 5 for y to get:
\n" ); document.write( "10x + 8*5 = 60 which becomes 10x + 40 = 60
\n" ); document.write( "subtract 40 from both sides to get:
\n" ); document.write( "10x = 20
\n" ); document.write( "divide both sides by 10 to get:
\n" ); document.write( "x = 2
\n" ); document.write( "---
\n" ); document.write( "you should now have your answer:
\n" ); document.write( "x = 2
\n" ); document.write( "y = 5
\n" ); document.write( "---
\n" ); document.write( "to prove, substitute for x and y in the first equation:
\n" ); document.write( "4x + 6y = 38
\n" ); document.write( "4*2 + 6*5 = 38
\n" ); document.write( "8 + 30 = 38
\n" ); document.write( "38 = 38
\n" ); document.write( "values for x and y are good.
\n" ); document.write( "---
\n" ); document.write( "since you used the second equation to find x, you don't need to check that equation again, but we'll do it anyway to show you.
\n" ); document.write( "10x + 8y = 60
\n" ); document.write( "10*2 + 8*5 = 60
\n" ); document.write( "20 + 40 = 60
\n" ); document.write( "60 = 60
\n" ); document.write( "values for x and y are good.
\n" ); document.write( "---
\n" ); document.write( "you could have eliminated the y and solved for x first. i just eliminated the x and solved for y first. either way would have worked.
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