document.write( "Question 217226: 1) Solve the system of linear equations
\n" ); document.write( " $\"system%28+x-2y%2B3z=-1%2C+4x%2B5y%2Bz=26%2C+-x%2By-2z=-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "a) What is the value of z?
\n" ); document.write( "b) What is the value of x?
\n" ); document.write( "c) What is the value of y? \n" ); document.write( "

Algebra.Com's Answer #163805 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"system%28+x-2y%2B3z=-1%2C+4x%2B5y%2Bz=26%2C+-x%2By-2z=-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "From the last equation -x+y-2z=-1, you quickly get x = y-2z+1.
\n" ); document.write( "substitute this in first two and simplify\r
\n" ); document.write( "\n" ); document.write( "first equation : (y-2z+1)-2y+3z=1 or -y+z=0
\n" ); document.write( "second equation: 4(y-2z+1)+5y+z=26, simplify this:
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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Graphical form: $\"4%2A%28y-2z%2B1%29%2B5y%2Bz=26\"$ simplifies to $\"9%2Ay-7%2Az-22=0\"$
Text form: 4*(y-2z+1)+5y+z=26 simplifies to 9*y-7*z-22=0
Cartoon (animation) form: $\"simplify_cartoon%28+4%2A%28y-2z%2B1%29%2B5y%2Bz=26+%29\"$
For tutors: simplify_cartoon( 4*(y-2z+1)+5y+z=26 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"4%2A%28y-2%2Az%2B1%29%2B5%2Ay%2Bz=highlight_red%28+26+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-26+%29\"$
It becomes $\"4%2A%28y-2%2Az%2B1%29%2B5%2Ay%2Bz-highlight_green%28+26+%29=0\"$ .
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Look at $\"highlight_red%28+4%2A%28y-2%2Az%2B1%29+%29%2B5%2Ay%2Bz-26=0\"$ .
Expanded term $\"4\"$ by using associative property on $\"%28y-2%2Az%2B1%29\"$
It becomes

.
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Look at $\"4%2Ay-highlight_red%28+4+%29%2Ahighlight_red%28+2+%29%2Az%2B4%2A1%2B5%2Ay%2Bz-26=0\"$ .
Multiplied numerator integers
It becomes $\"4%2Ay-highlight_green%28+8+%29%2Az%2B4%2A1%2B5%2Ay%2Bz-26=0\"$ .
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Look at $\"4%2Ay-8%2Az%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+1+%29%2B5%2Ay%2Bz-26=0\"$ .
Multiplied numerator integers
It becomes $\"4%2Ay-8%2Az%2Bhighlight_green%28+4+%29%2B5%2Ay%2Bz-26=0\"$ .
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Look at $\"4%2Ay-8%2Az%2Bhighlight_red%28+4+%29%2B5%2Ay%2Bz-highlight_red%28+26+%29=0\"$ .
Added fractions or integers together
It becomes $\"4%2Ay-8%2Az%2Bhighlight_green%28+-22+%29%2B5%2Ay%2Bz=0\"$ .
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Look at $\"4%2Ay-8%2Az%2Bhighlight_red%28+-22+%29%2B5%2Ay%2Bz=0\"$ .
Moved $\"-22\"$ to the right of expression
It becomes $\"4%2Ay-8%2Az%2B5%2Ay%2Bz%2Bhighlight_green%28+-22+%29=0\"$ .
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Look at $\"4%2Ay-8%2Az%2B5%2Ay%2Bz%2Bhighlight_red%28+-22+%29=0\"$ .
Removed extra sign in front of $\"-22\"$
It becomes $\"4%2Ay-8%2Az%2B5%2Ay%2Bz-highlight_green%28+22+%29=0\"$ .
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Look at $\"highlight_red%28+4%2Ay+%29-8%2Az%2Bhighlight_red%28+5%2Ay+%29%2Bz-22=0\"$ .
Eliminated similar terms $\"highlight_red%28+4%2Ay+%29\"$ , $\"highlight_red%28+5%2Ay+%29\"$ replacing them with $\"highlight_green%28+%284%2B5%29%2Ay+%29\"$
It becomes $\"highlight_green%28+%284%2B5%29%2Ay+%29-8%2Az%2Bz-22=0\"$ .
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Look at $\"%284%2B5%29%2Ay-highlight_red%28+8%2Az+%29%2Bhighlight_red%28+z+%29-22=0\"$ .
Eliminated similar terms $\"highlight_red%28+-8%2Az+%29\"$ , $\"highlight_red%28+z+%29\"$ replacing them with $\"highlight_green%28+%28-8%2B1%29%2Az+%29\"$
It becomes $\"%284%2B5%29%2Ay%2Bhighlight_green%28+%28-8%2B1%29%2Az+%29-22=0\"$ .
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Look at $\"%28highlight_red%28+4+%29%2Bhighlight_red%28+5+%29%29%2Ay%2B%28-8%2B1%29%2Az-22=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+9+%29%29%2Ay%2B%28-8%2B1%29%2Az-22=0\"$ .
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Look at $\"%289%29%2Ay%2B%28-highlight_red%28+8+%29%2Bhighlight_red%28+1+%29%29%2Az-22=0\"$ .
Added fractions or integers together
It becomes $\"%289%29%2Ay%2B%28highlight_green%28+-7+%29%29%2Az-22=0\"$ .
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Look at $\"%289%29%2Ay%2B%28highlight_red%28+-7+%29%29%2Az-22=0\"$ .
Removed extra sign in front of $\"-7\"$
It becomes $\"%289%29%2Ay%2B%28-highlight_green%28+7+%29%29%2Az-22=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+9+%29%29%2Ay+%29%2B%28-7%29%2Az-22=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+9+%29\"$
It becomes $\"highlight_green%28+9+%29%2Ay%2B%28-7%29%2Az-22=0\"$ .
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Look at $\"9%2Ay%2Bhighlight_red%28+%28-highlight_red%28+7+%29%29%2Az+%29-22=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$
It becomes $\"9%2Ay-highlight_green%28+7+%29%2Az-22=0\"$ .
Result: $\"9%2Ay-7%2Az-22=0\"$
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Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "so we get $\"+system%28+-y%2Bz=0%2C+9y-7z=22%29+\"$ \r
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Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
\n" ); document.write( " $\"+system%28+%0D%0A++++-1%5Cy+%2B+1%5Cz+=+0%2C%0D%0A++++9%5Cy+%2B+-7%5Cz+=+22+%29%0D%0A++\"$ We'll use substitution. After moving 1*z to the right, we get:
\n" ); document.write( " $\"-1%2Ay+=+0+-+1%2Az\"$ , or $\"y+=+0%2F-1+-+1%2Az%2F-1\"$ . Substitute that
\n" ); document.write( " into another equation:
\n" ); document.write( " $\"9%2A%280%2F-1+-+1%2Az%2F-1%29+%2B+-7%5Cz+=+22\"$ and simplify: So, we know that z=11. Since $\"y+=+0%2F-1+-+1%2Az%2F-1\"$ , y=11.
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\n" ); document.write( " Answer: $\"system%28+y=11%2C+z=11+%29\"$ .
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\n" ); document.write( "\n" ); document.write( "Since y and z = 11, and x = y-2z+1, we get x = 11-22+1 = -10 \n" ); document.write( "

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