NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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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
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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

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