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Video: Solving a System of Linear Equations in Two Unknowns

Bethani Gasparine

Solve the simultaneous equations 2x+y=11 and x-2y=3.


Video Transcript

Solve the simultaneous equations, two π‘₯ plus 𝑦 equals eleven and π‘₯ minus two 𝑦 equals three.

Now we’re gonna be using the elimination method. In order to use the elimination method, we will stack these equations where the π‘₯s make a column, the 𝑦s make a column, and our constants make a column. And we will eventually be adding these together. However, we wanna add them together, so that way one of the variables wipeout, it disappears.

So in order to do that, we’re gonna have to multiply one of these equations by a number. And we can either choose to eliminate π‘₯ or eliminate 𝑦. Looking at the 𝑦s, we have a positive 𝑦 and a negative two 𝑦. Those would cancel if that 𝑦 was a two 𝑦 because two 𝑦 minus two 𝑦 would make them cancel. So we need to multiply the top equation by two. And doing so, we get four π‘₯ plus two 𝑦 equals twenty-two.

And now we bring our other equation over. And now we can add them together. Four π‘₯ plus π‘₯ is five π‘₯. Two 𝑦 minus two 𝑦 is zero; they just cancel. And then twenty-two plus three is twenty-five. So we have five π‘₯ equals twenty-five. So we need now to divide both sides by five, resulting in π‘₯ equals five.

So now that we have a value for π‘₯, we can take that and plug it in to either of the equations we had in our question. So again, we can plug it in either equation. Let’s go ahead and plug it in the π‘₯ minus two 𝑦 equals three. And instead of π‘₯, we will replace π‘₯ with five. So now we need to subtract five from both sides, so we have negative two 𝑦 equals negative two. Now divide both sides by negative two, and we get that 𝑦 equals positive one.

So π‘₯ equals five and 𝑦 equals one.