 iGCSE (2021 Edition)

3.09 Elimination method for simultaneous equations

Interactive practice questions

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

 Equation 1 $8x+3y=19$8x+3y=19 Equation 2 $3x-3y=25$3x−3y=25
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

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 $x=4$x=4 into either of the equations and solve for $y$y.

Enter each line of working as an equation.

Easy
Approx 4 minutes

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

 Equation 1 $3x+4y=12$3x+4y=12 Equation 2 $-3x+6y=18$−3x+6y=18

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=3$5x+3y=3

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

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

Outcomes

0606C6.1

Solve simple simultaneous equations in two unknowns by elimination or substitution.