Video: Solving a System of Linear Equations in Two Unknowns

Find π‘₯, given 2π‘₯ βˆ’ 𝑦 = 5 and 𝑦 = 7π‘₯.

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Video Transcript

Find π‘₯, given two π‘₯ minus 𝑦 equals five and 𝑦 equals seven π‘₯.

Substituting the second equation 𝑦 equals seven π‘₯ into the first equation eliminates the 𝑦. And we are left with two π‘₯ minus seven π‘₯ equals five. Two π‘₯ minus seven π‘₯ is negative five π‘₯. Dividing both sides of this equation by negative five gives us π‘₯ equals negative one. This is because negative five π‘₯ divided by negative five is π‘₯ and five divided by negative five is negative one. Therefore, the value of π‘₯ that satisfies both of the equations two π‘₯ minus 𝑦 equals five and 𝑦 equals seven π‘₯ is π‘₯ equals negative one.

Whilst we’ve not been asked to work out the 𝑦-value in this question, we could do so by substituting our value of π‘₯, negative one, into either one of the equations. If we substituted it into the equation 𝑦 equals seven π‘₯, then 𝑦 would be equal to seven multiplied by negative one. 𝑦 therefore is equal to negative seven. We could check that these answers are correct by substituting them into equation one: two π‘₯ minus 𝑦 equals five.

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