# Video: Solving Simultaneous Using Elimination Where One of the Equations Needs to be Multiplied

Using elimination, solve the simultaneous equations 3π₯ + 7π¦ = 34, 9π₯ + 10π¦ = 91.

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### 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, Iβm 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, weβre 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.