### Video Transcript

Using elimination, solve the
simultaneous equations three π₯ plus seven π¦ equals 34 and nine π₯ plus 10 π¦
equals 91.

Our first step is to make either
the π₯ or the π¦ coefficients the same. In this case, the easiest way to do
this is to multiply the first equation by three. Multiplying three π₯ by three gives
us nine π₯. Multiplying seven π¦ by three gives
us 21 π¦. And 34 multiplied by three is
102.

If we then subtract equation two
from equation one, the π₯ terms cancel as nine π₯ minus nine π₯ is zero. 21 π¦ minus 10 π¦ is equal to 11
π¦. And 102 minus 91 is equal to
11. Dividing both sides of this
equation by 11 gives us an answer for π¦ equal to one.

In order to work out our value for
π₯, we need to substitute this value for π¦ into one of the equations. In this case, Iβm going to
substitute π¦ equals one into equation two. Substituting in this value for π¦
gives us nine π₯ plus 10 multiplied by one equals 91.

As 10 multiplied by one is 10,
weβre left with nine π₯ plus 10 equals 91. We can then subtract 10 from both
sides of the equation, leaving us nine π₯ is equal to 81. And finally dividing both sides of
this equation by nine leaves as a value for π₯ equal to nine.

Therefore, the solution to the
simultaneous equations three π₯ plus seven π¦ equals 34 and nine π₯ plus 10 π¦
equals 91 are π¦ equals one and π₯ equals nine.

We could check these two answers by
substituting the values of π₯ and π¦ 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.