// Numbas version: exam_results_page_options {"name": "Simultaneous equations by substitution 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "ans1", "ans2", "ans3", "yCoef", "n1", "n2", "n3", "n4"], "name": "Simultaneous equations by substitution 2", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.

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We start by rearranging equation (1) like so:

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$\\simplify{y = 1/{n2}*({ans1}-{n1}*x)}$

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$\\simplify{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) = {ans2}}$

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$\\simplify{({n3}-{n1}*{n4}/{n2})*x + {n4}*{ans1}/{n2} = {ans2}}$

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$\\simplify{x=({n4}*{ans1}-{n2}*{ans2})/({n1}*{n4}-{n3}*{n2})}$

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Substitute the value of x back into equation (1) to find

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$\\simplify{y=({ans1}*{n3}-{n1}*{ans2})/({n2}*{n3}-{n1}*{n4})}$

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Solve the pair of equations

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\$\\begin{eqnarray} \\simplify{{n1}*x + {n2}*y} & = & \\var{ans1} &&&&&&&(1)\\\\ \\simplify{{n3}*x + {n4}*y} & = & \\var{ans2}&&&&&&&(2)\\end{eqnarray}\$

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We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.

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We start by rearranging equation (1) like so:

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$y =$[[0]],      (3)

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Substitute equation (3) into equation (2) to give:

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[[1]]$\\simplify{x + {n4}*{ans1}/{n2} = {ans2}}$

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Solve this linear equation to give  $x =$[[2]],

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Substitute the value of x back into equation (1) to find

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$y =$[[3]]

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Straightforward solving linear equations question

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