NZ Level 8 (NZC) Level 3 (NCEA) [In development] Linear Systems in Three Unknowns

## Interactive practice questions

We want to determine if the ordered triple $\left(-9,-7,4\right)$(9,7,4) is a solution of the following system of equations.

 $-2x$−2x $+$+ $5y$5y $-$− $3z$3z $=$= $-29$−29 $-3x$−3x $+$+ $y$y $+$+ $4z$4z $=$= $38$38 $-4x$−4x $+$+ $2y$2y $+$+ $3z$3z $=$= $34$34
a

Find the missing values by substituting in the ordered triple $\left(-9,-7,4\right)$(9,7,4).

 $-2x$−2x $+$+ $5y$5y $-$− $3z$3z $=$= $\editable{}$ $-3x$−3x $+$+ $y$y $+$+ $4z$4z $=$= $\editable{}$ $-4x$−4x $+$+ $2y$2y $+$+ $3z$3z $=$= $\editable{}$
b

Is the ordered triple $\left(-9,-7,4\right)$(9,7,4) a solution of the system of equations?

Yes

A

No

B

Yes

A

No

B
Easy
Approx 4 minutes

We want to determine if the ordered triple $\left(1,-5,-3\right)$(1,5,3) is a solution of the following system of equations.

 $4x$4x $-$− $5y$5y $+$+ $3z$3z $=$= $20$20 $4x$4x $-$− $5y$5y $-$− $z$z $=$= $32$32 $-x$−x $+$+ $2y$2y $-$− $5z$5z $=$= $4$4

Is the ordered triple $\left(\frac{3}{4},\frac{4}{5},\frac{2}{5}\right)$(34,45,25) a solution of the following system?

 $5x$5x $+$+ $y$y $+$+ $3z$3z $=$= $\frac{23}{4}$234​ $4x$4x $+$+ $3y$3y $+$+ $5z$5z $=$= $\frac{37}{5}$375​ $2x$2x $-$− $4y$4y $+$+ $3z$3z $=$= $-\frac{1}{2}$−12​

Is the ordered triple $\left(1.1,0.3,1.7\right)$(1.1,0.3,1.7) a solution of the following system?

 $3x$3x $+$+ $y$y $-$− $5z$5z $=$= $-5.9$−5.9 $5x$5x $+$+ $y$y $-$− $4z$4z $=$= $-1$−1 $5x$5x $-$− $2y$2y $-$− $4z$4z $=$= $-1.9$−1.9

### 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