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Since the matrices are equal, the corresponding elements are equal.
\Write two linear equations.
\x + 3y = –22
\2x – y = 19
\![\"\"](\"/userfiles/image/steps_images/step2.JPG\")
Consider the second equation
\2x – y=19
\2x – y + y= 19 + y \ \
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Substitute ![\"\"](\"http://c4anything.com/MathKey/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4b9892ebe2e26cf9dc1ea80b5883d1f2.png\")
in x + 3y = – 22
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19 + y + 6y = –44 (Multiply each side by 2)
\19 + 7y = –44 (Add: 6y + y = 7y)
\19 -19 + 7y = –44 – 19 (Subtraction 19 from each side)
\7y = – 63 (Subtract: – 44 –19 = – 63)
\![\"\"](\"/MathKey/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=82dc5ee36d5fbff23ba20bba75b0fd60.png\")
(Divide each side by 7)
y = – 9 (Simplify)
\![\"\"](\"/userfiles/image/steps_images/step3.JPG\")
To find the value of x, substitute – 9 for y in either equation.
\2x – y = 19
\2x + 9 = 19 (Substitute –9 for y)
\2x + 9 – 9 = 19 – 9 (Subtract 9 from each side)
\2x = 10 (Subtract: 19 – 9 = 10)
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(Divide each side by 2)
x = 5 (Simplify)
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The solution is (5,-9)
\