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3.09 The elimination method

Interactive practice questions

Given the following equations, we want to solve for $x$x and $y$y using the elimination method.

Equation 1 $6x+3y=3$6x+3y=3
Equation 2 $5x-3y=30$5x3y=30
a

Notice that Equation 1 has a $3y$3y term and Equation 2 has a $-3y$3y term. How can we combine the equations to eliminate the $y$y-terms?

Equation 1 $+$+$2\times$2× Equation 2

A

$2\times$2× Equation 1 $-$ Equation 2

B

Equation 1 $+$+ Equation 2

C

Equation 1 $-$ Equation 2

D
b

Solve for $x$x by adding Equations 1 and 2 together.

Enter each line of working as an equation.

c

Substitute $x=3$x=3 into either of the equations and solve for $y$y.

Enter each line of working as an equation.

Easy
3min

Given the following equations, we want to solve for $x$x and $y$y using the elimination method.

Equation 1 $3x+2y=-3$3x+2y=3
Equation 2 $-3x+6y=27$3x+6y=27
Easy
2min

Given the following equations, we want to solve for $x$x and $y$y using the elimination method.

Equation 1 $8x+3y=-9$8x+3y=9
Equation 2 $5x+3y=0$5x+3y=0
Easy
2min

Given the following equations, we want to solve for $x$x and $y$y using the elimination method.

Equation 1 $x+6y=-2$x+6y=2
Equation 2 $x+3y=-5$x+3y=5
Easy
3min
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Outcomes

VCMNA337

Solve simultaneous linear equations, using algebraic and graphical techniques including using digital technology

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