Find 𝑥, given two 𝑥 minus 𝑦 equals five and 𝑦 equals seven 𝑥.
Substituting the second equation 𝑦 equals seven 𝑥 into the first equation eliminates the 𝑦. And we are left with two 𝑥 minus seven 𝑥 equals five. Two 𝑥 minus seven 𝑥 is negative five 𝑥. Dividing both sides of this equation by negative five gives us 𝑥 equals negative one. This is because negative five 𝑥 divided by negative five is 𝑥 and five divided by negative five is negative one. Therefore, the value of 𝑥 that satisfies both of the equations two 𝑥 minus 𝑦 equals five and 𝑦 equals seven 𝑥 is 𝑥 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 𝑥, negative one, into either one of the equations. If we substituted it into the equation 𝑦 equals seven 𝑥, 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 𝑥 minus 𝑦 equals five.