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New Zealand
Level 8 - NCEA Level 3

Problems with Simultaneous Equations

Interactive practice questions

The sum of two numbers is $56$56 and their difference is $30$30.


Set up two equations by letting $x$x and $y$y be the two numbers.

Use $x$x as the larger of the 2 numbers.

Sum equation: $\editable{}$
Difference equation: $\editable{}$

First solve for $x$x

Equation 1 $x+y=56$x+y=56
Equation 2 $x-y=30$xy=30

Now solve for $y$y

Approx 3 minutes
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The length of a rectangle measures $12$12 units more than the width, and the perimeter of the rectangle is $56$56 units.

Let $y$y be the width and $x$x be the length of the rectangle.

There are $36$36 members in a group, and the men outnumber the women by $16$16.

When comparing some test results Christa noticed that the sum of her Geography test score and Science test score was $172$172, and that their difference was $18$18.

Given that her Geography score is $x$x and her Science score is $y$y and she scored higher for the Geography test:



Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context


Apply systems of simultaneous equations in solving problems

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