Video Transcript
Using elimination, solve the
simultaneous equations three 𝑥 plus seven 𝑦 equals 34 and nine 𝑥 plus 10 𝑦
equals 91.
Our first step is to make either
the 𝑥 or the 𝑦 coefficients the same. In this case, the easiest way to do
this is to multiply the first equation by three. Multiplying three 𝑥 by three gives
us nine 𝑥. Multiplying seven 𝑦 by three gives
us 21 𝑦. And 34 multiplied by three is
102.
If we then subtract equation two
from equation one, the 𝑥 terms cancel as nine 𝑥 minus nine 𝑥 is zero. 21 𝑦 minus 10 𝑦 is equal to 11
𝑦. And 102 minus 91 is equal to
11. Dividing both sides of this
equation by 11 gives us an answer for 𝑦 equal to one.
In order to work out our value for
𝑥, we need to substitute this value for 𝑦 into one of the equations. In this case, I’m going to
substitute 𝑦 equals one into equation two. Substituting in this value for 𝑦
gives us nine 𝑥 plus 10 multiplied by one equals 91.
As 10 multiplied by one is 10,
we’re left with nine 𝑥 plus 10 equals 91. We can then subtract 10 from both
sides of the equation, leaving us nine 𝑥 is equal to 81. And finally dividing both sides of
this equation by nine leaves as a value for 𝑥 equal to nine.
Therefore, the solution to the
simultaneous equations three 𝑥 plus seven 𝑦 equals 34 and nine 𝑥 plus 10 𝑦
equals 91 are 𝑦 equals one and 𝑥 equals nine.
We could check these two answers by
substituting the values of 𝑥 and 𝑦 back into the other equation, number one. Nine multiplied by nine plus 21
multiplied by one is equal to 102. Therefore, our solution is
correct.
