NZ Level 6 (NZC) Level 1 (NCEA)
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The Elimination Method

Interactive practice questions

Consider this system of equations.

Equation 1 $\frac{4x}{5}+\frac{3y}{5}=4$4x5+3y5=4
Equation 2

$8x-3y=5$8x3y=5

Which operation will change the fractional coefficients to integer coefficients in this system of equations?

Multiply Equation 2 by $5$5.

A

Multiply Equation 1 by $5$5.

B

Divide Equation 2 by $3$3.

C

Divide Equation 1 by $3$3.

D

Multiply Equation 2 by $5$5.

A

Multiply Equation 1 by $5$5.

B

Divide Equation 2 by $3$3.

C

Divide Equation 1 by $3$3.

D
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Consider this system of equations.

Equation 1 $\frac{2x}{5}+\frac{3y}{5}=-\frac{7}{5}$2x5+3y5=75
Equation 2

$-\frac{1}{4}\left(-5x+\frac{7y}{9}\right)=2$14(5x+7y9)=2

Consider the following system of equations.

Equation 1 $3x+7y=-6$3x+7y=6
Equation 2 $2x-y=-17$2xy=17

Suppose we want to solve this system by using the elimination method and eliminating $y$y.

Consider the following system of equations.

$-8x$8x $-$ $y$y $=$= $0$0
$-5x$5x $+$+ $3y$3y $=$= $6$6

Suppose we solve this system using the elimination method by multiplying both sides of the first equation by $3$3 and then adding the resulting equation to the second equation. What equation do we get?

Do not solve the equation.

Outcomes

NA6-5

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

91027

Apply algebraic procedures in solving problems

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