Test your knowledge! Which method is useful to solve the following systems of equations?
II3x+6y=2\hphantom{\mathrm{I}}\mathrm{I} \quad 3x + 6y = 2II3x+6y=2
II4x+2=y\mathrm{II} \quad 4x + 2 = yII4x+2=y
substitution method
equating coefficients
addition method
Für diese Aufgabe benötigst Du folgendes Grundwissen: System of linear equations
The equation II\mathrm{II}II is already solved for yyy. Therefore, the substitution method is advisable.
The other two methods also get you to the goal, but they require further transformation steps.
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IIs=4t−7\hphantom{\mathrm{I}}\mathrm{I} \quad s = 4t -7IIs=4t−7
IIs=−2+3t\mathrm{II} \quad s = -2 + 3tIIs=−2+3t
All three methods can be applied directly and are useful for this reason.
II2a−2b=3\hphantom{\mathrm{I}}\mathrm{I} \quad 2a - 2b = 3II2a−2b=3
II5a+2b=6\mathrm{II} \quad 5a + 2b = 6II5a+2b=6
Equation I\mathrm{I}I contains −2b-2b−2b, equation II\mathrm{II}II contains 2b2b2b. So the bbb will drop out when adding both lines, which makes the addition method suitable.
With the other two procedures, you have to take further transformation steps, before one can apply them.
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