document.write( "Question 603807: 5x -3y = 17
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Algebra.Com's Answer #380842 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!
 
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\n" ); document.write( "5x -3y = 17
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\n" ); document.write( "\n" ); document.write( "Applying Cramers rule
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Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables

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\n" ); document.write( " \"system%285%2Ax%2B-3%2Ay=17%2C-2%2Ax%2B5%2Ay=-22%29\"
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\n" ); document.write( " First let \"A=%28matrix%282%2C2%2C5%2C-3%2C-2%2C5%29%29\". This is the matrix formed by the coefficients of the given system of equations.
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\n" ); document.write( " Take note that the right hand values of the system are \"17\" and \"-22\" which are highlighted here:
\n" ); document.write( " \"system%285%2Ax%2B-3%2Ay=highlight%2817%29%2C-2%2Ax%2B5%2Ay=highlight%28-22%29%29\"
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\n" ); document.write( " These values are important as they will be used to replace the columns of the matrix A.
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\n" ); document.write( " Now let's calculate the the determinant of the matrix A to get \"abs%28A%29=%285%29%285%29-%28-3%29%28-2%29=19\". Remember that the determinant of the 2x2 matrix \"A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\" is \"abs%28A%29=ad-bc\". If you need help with calculating the determinant of any two by two matrices, then check out this solver.
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\n" ); document.write( " Notation note: \"abs%28A%29\" denotes the determinant of the matrix A.
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\n" ); document.write( " Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix \"A%5Bx%5D\" (since we're replacing the 'x' column so to speak).
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\n" ); document.write( " \"A%5Bx%5D=%28matrix%282%2C2%2Chighlight%2817%29%2C-3%2Chighlight%28-22%29%2C5%29%29\"
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\n" ); document.write( " Now compute the determinant of \"A%5Bx%5D\" to get \"abs%28A%5Bx%5D%29=%2817%29%285%29-%28-3%29%28-22%29=19\". Once again, remember that the determinant of the 2x2 matrix \"A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\" is \"abs%28A%29=ad-bc\"
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\n" ); document.write( " To find the first solution, simply divide the determinant of \"A%5Bx%5D\" by the determinant of \"A\" to get: \"x=%28abs%28A%5Bx%5D%29%29%2F%28abs%28A%29%29=%2819%29%2F%2819%29=1\"
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\n" ); document.write( " So the first solution is \"x=1\"
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\n" ); document.write( " We'll follow the same basic idea to find the other solution. Let's reset by letting \"A=%28matrix%282%2C2%2C5%2C-3%2C-2%2C5%29%29\" again (this is the coefficient matrix).
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\n" ); document.write( " Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix \"A%5By%5D\" (since we're replacing the 'y' column in a way).
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\n" ); document.write( " \"A%5Bx%5D=%28matrix%282%2C2%2C5%2Chighlight%2817%29%2C-2%2Chighlight%28-22%29%29%29\"
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\n" ); document.write( " Now compute the determinant of \"A%5By%5D\" to get \"abs%28A%5By%5D%29=%285%29%28-22%29-%2817%29%28-2%29=-76\".
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\n" ); document.write( " To find the second solution, divide the determinant of \"A%5By%5D\" by the determinant of \"A\" to get: \"y=%28abs%28A%5By%5D%29%29%2F%28abs%28A%29%29=%28-76%29%2F%2819%29=-4\"
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\n" ); document.write( " So the second solution is \"y=-4\"
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\n" ); document.write( " Final Answer:
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\n" ); document.write( " So the solutions are \"x=1\" and \"y=-4\" giving the ordered pair (1, -4)
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\n" ); document.write( " Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.
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