Solve the following simultaneous equations for $x$ and $y$. Input your answers as fractions or integers, not as decimals.
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", "notes": "5/08/2012:
\nAdded more tags.
\nAdded description.
\nChecked calculation. OK.
", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "prompt": "\\[ \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&=&\\var{c}\\\\ \\simplify[std]{{a1}x+{b1}y}&=&\\var{c1} \\end{eqnarray} \\]
\n$x=\\phantom{{}}$[[0]], $y=\\phantom{{}}$[[1]]
\nInput your answers as fractions or integers, not as decimals.
", "gaps": [{"marks": 1, "notallowed": {"partialCredit": 0, "strings": ["."], "message": "Input as a fraction or an integer not as a decimal
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", "showStrings": false}, "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "answersimplification": "std", "checkvariablenames": false, "vsetrangepoints": 5, "showpreview": true, "scripts": {}, "checkingaccuracy": 0.001, "type": "jme", "vsetrange": [0, 1], "answer": "{c*a1-a*c1}/{b*a1-a*b1}"}]}], "type": "question", "advice": "\\[ \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&=&\\var{c}&\\mbox{ ........(1)}\\\\ \\simplify[std]{{a1}x+{b1}y}&=&\\var{c1}&\\mbox{ ........(2)} \\end{eqnarray} \\]
To get a solution for $x$ multiply equation (1) by {this} and equation (2) by {that}
This gives:
\\[ \\begin{eqnarray} \\simplify[std]{{a*this}x+{b*this}y}&=&\\var{this*c}&\\mbox{ ........(3)}\\\\ \\simplify[std]{{a1*that}x+{b1*that}y}&=&\\var{that*c1}&\\mbox{ ........(4)} \\end{eqnarray} \\]
Now {aort} (4) {fromorto} equation (3) to get
\\[\\simplify[std]{({a*this}+{s6*a1*that})x={this*c}+{s6*that*c1}}\\]
And so we get the solution for $x$:
\\[x = \\simplify{{c*b1-b*c1}/{b1*a-a1*b}}\\]
Substituting this value into any of the equations (1) and (2) gives:
\\[y = \\simplify{{c*a1-a*c1}/{b*a1-a*b1}}\\]
You can check that these solutions are correct by seeing if they satisfy both equations (1) and (2) by substituting these values into the equations.