3. Equations and Inequalities

iGCSE (2021 Edition)

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$3`y` term and Equation 2 has a $-3y$−3`y` 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

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