NZ Level 6 (NZC) Level 1 (NCEA) Problems with Simultaneous Equations

## Interactive practice questions

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

a

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: $\editable{}$
b

First solve for $x$x

 Equation 1 $x+y=56$x+y=56 Equation 2 $x-y=30$x−y=30
c

Now solve for $y$y

Easy
Approx 3 minutes

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:

### Outcomes

#### NA6-5

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

#### NA6-7

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

#### 91027

Apply algebraic procedures in solving problems

#### 91028

Investigate relationships between tables, equations and graphs