1/2(x+2y)+5/3(3x-2y) = -3/2
5/4(x+2y)-3/5(3x-2y)= 61/60
Answers
Answer:
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
AO elaboration and other teaching resources
NA5-7: Form and solve linear and simple quadratic equations.
AO elaboration and other teaching resources
Student Activity

Tui realises that there are nine positions in a magic square.
Can she make up a magic square using each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 only once?
Specific Learning Outcomes
Use algebra as required
Construct magic squares
Description of Mathematics
A magic square is an arrangement like the one below where the vertical, horizontal and diagonal lines of numbers all add up to the same value. This ‘same value’ is called the sum of the magic square.
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It’s a critical part of this problem that three times the centre square is equal to the sum of the magic square. Developing the proof is the point of this lesson. This is also proved in the Extension to Negative Magic Squares, Level 4.
The magic square in this problem can be solved by guess and check. Using algebra is however the more efficient way. Students should be encouraged to determine what critical information within the problem is needed in order to find a solution, allowing the students to develop their own algebraic equations to fit the problem situation.