Multiply the first equation by $\\var{b1}$ and the second equation by $\\var{b}$ so they both have the same $y$ coefficient:
\n\\begin{align}
\\simplify{{a*b1}x+{b*b1}y} &= \\var{c*b1} \\\\
\\simplify{{a1*b}x+{b1*b}y} &= \\var{c1*b}
\\end{align}
Next, subtract the second equation from the first to get
\n\\[ \\simplify[std]{{a*b1-a1*b}x} = \\var{c*b1-c1*b} \\]
\nSo $x = \\simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}$.
\nSubstitute this value of $x$ into the first equation and rearrange to obtain $y$:
\n\\begin{align}
\\simplify[std]{{a}*{(c*b1-c1*b)/(a*b1-a1*b)} + {b}y} &= \\var{c} \\\\
\\simplify[std]{{b}y} &= \\simplify[std]{{c}-{a*(c*b1-c1*b)/(a*b1-a1*b)}} \\\\
y &= \\simplify[std]{{(c-a*(c*b1-c1*b)/(a*b1-a1*b))/b}}
\\end{align}
\\[\\begin{eqnarray*} \\simplify{{a}x+{b}y}&=&\\var{c}\\\\\\\\\\simplify{{a1}x+{b1}y}&=&\\var{c1}\\end{eqnarray*}\\]
\n$x=$ [[0]]
\n$y=$ [[1]]
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\n$x=$ [[0]]
\n$y=$ [[1]]
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"}, "variables": {"c1": {"templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables", "name": "c1", "description": ""}, "a": {"templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables", "name": "c", "description": ""}, "a3": {"templateType": "anything", "definition": "random(1..9 except[a,a1])", "group": "Ungrouped variables", "name": "a3", "description": ""}, "c3": {"templateType": "anything", "definition": "random(1..9 except c1)", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c4": {"templateType": "anything", "definition": "random(1..9 except [c,c1,c2,c3])", "group": "Question 3", "name": "c4", "description": ""}, "a4": {"templateType": "anything", "definition": "random(1..9 except[a,a1,a2,a3])", "group": "Question 3", "name": "a4", "description": ""}, "c2": {"templateType": "anything", "definition": "random(1..9 except [c,c1])", "group": "Ungrouped variables", "name": "c2", "description": ""}, "b1": {"templateType": "anything", "definition": "random(1..9 except round(a1*b/a))", "group": "Ungrouped variables", "name": "b1", "description": ""}, "a5": {"templateType": "anything", "definition": "random(1..9 except[a,a1,a2,a3,a4])", "group": "Question 3", "name": "a5", "description": ""}, "b5": {"templateType": "anything", "definition": "random(1..9 except round(a5*b4/a4))", "group": "Question 3", "name": "b5", "description": ""}, "b4": {"templateType": "anything", "definition": "random(-9..9 except [0,a4])", "group": "Question 3", "name": "b4", "description": ""}, "b": {"templateType": "anything", "definition": "random(-9..9 except [0,a])", "group": "Ungrouped variables", "name": "b", "description": ""}, "a1": {"templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b3": {"templateType": "anything", "definition": "random(1..9 except round(a3*b2/a2))", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c5": {"templateType": "anything", "definition": "random(1..9 except [c1,c3])", "group": "Question 3", "name": "c5", "description": ""}, "a2": {"templateType": "anything", "definition": "random(1..9 except [a,a1])", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b2": {"templateType": "anything", "definition": "random(-9..9 except [0,a2])", "group": "Ungrouped variables", "name": "b2", "description": ""}}, "rulesets": {"std": ["All", "fractionnumbers"]}, "preamble": {"css": "", "js": ""}, "statement": "Solve the following pair of simultaneous equations. You should write your answer as a simplified fraction in the form a/b, e.g. 3/4 or 12/5.
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