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New Zealand
Level 6 - NCEA Level 1

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 solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns


Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns


Apply algebraic procedures in solving problems


Investigate relationships between tables, equations and graphs

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