# Question Video: Solving a System of Linear Equations in Two Unknowns Mathematics • 8th Grade

Find π₯, given 2π₯ β π¦ = 5 and π¦ = 7π₯.

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### Video Transcript

Find π₯, given two π₯ minus π¦ equals five and π¦ equals seven π₯.

Substituting the second equation π¦ equals seven π₯ into the first equation eliminates the π¦. 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 π¦ equals five and π¦ equals seven π₯ is π₯ equals negative one.

Whilst weβve not been asked to work out the π¦-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 π¦ equals seven π₯, then π¦ would be equal to seven multiplied by negative one. π¦ therefore is equal to negative seven. We could check that these answers are correct by substituting them into equation one: two π₯ minus π¦ equals five.