# GCSE Higher Level Solving Simultaneous equations:

**Elimination method:**

2X + 5Y =2 (-3)

3X + 8Y = 4 (2)

In order to reduce the x term we need to make it have the same coefficient as the other equation, so we multiply the first one by -3 and the next one by 2

-3 x 2X -3 x 5Y= -3 x 2 => -6X – 15Y = -6

2 x 3X + 2 x 8Y = 2 x 4 => 6X + 16Y = 8

0 + Y = 2 => Y=2

After finding Y we can replace it in any of the two equations to find out X:

2X + 5 x 2 = 2 => 2X + 10 = 2

2X= -8 => X= -8/2= > X= -4

**Substitution method:**

Substitution method is applied when the terms are too big to be reduced. First one of the terms needs to be arranged as a dependent of the other term: X+Y=-2 => X=-2-Y 2X – 3X = 11

2(-Y-2)- 3Y= 11

-2Y- 4 -3Y=11

-5Y- 4= 11

-5Y= 15

Y=-3

Now to find out X replace it in one of the equations:

X-3= -2

X= -2+3

X=1

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