NZ Level 8 (NZC) Level 3 (NCEA) [In development] Examine solutions to systems of equations in 3 unknowns

## Interactive practice questions

Consider the following system of 3 equations:

 $8x$8x $+$+ $3y$3y $+$+ $7z$7z $=$= $\frac{160}{9}$1609​ $24x$24x $+$+ $9y$9y $+$+ $21z$21z $=$= $\frac{320}{9}$3209​ $3x$3x $+$+ $8y$8y $+$+ $8z$8z $=$= $\frac{160}{3}$1603​
a

The system has:

One solution.

A

No Solution.

B

Infinite solutions.

C

One solution.

A

No Solution.

B

Infinite solutions.

C
b

The system is:

Consistent

A

Inconsistent

B

Consistent

A

Inconsistent

B
Easy
Less than a minute

Consider the following system of equation:

 $6x$6x $+$+ $5y$5y $+$+ $2z$2z $=$= $14$14 $30x$30x $+$+ $25y$25y $+$+ $10z$10z $=$= $70$70 $18x$18x $+$+ $15y$15y $+$+ $6z$6z $=$= $42$42

Consider the following system of three equations:

 $9x$9x $+$+ $9y$9y $+$+ $9z$9z $=$= $135$135 $45x$45x $+$+ $45y$45y $+$+ $45z$45z $=$= $675$675 $x$x $+$+ $y$y $+$+ $z$z $=$= $15$15

Consider the following system of 3 equations:

 $2x$2x $+$+ $9y$9y $+$+ $\frac{2}{14}z$214​z $=$= $3$3 ----- equation $1$1 $6x$6x $+$+ $27y$27y $+$+ $\frac{3}{7}z$37​z $=$= $9$9 ----- equation $2$2 $8x$8x $+$+ $36y$36y $+$+ $\frac{4}{7}z$47​z $=$= $12$12 ----- equation $3$3

### Outcomes

#### M8-8

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

#### 91587

Apply systems of simultaneous equations in solving problems