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 Question from Steve, a student: Verify solutions to an equation in two variables. 4x-2y=8 (3, 2)

Hi Steve,

Let me illustrate with a different expression, $7x - 4y = 7.$

You are then given a pair of numbers, say $(5, 7)$ and asked if this pair of numbers is a solution of $7x - 4y = 7.$

In your question, for the par of numbers $(3, 2)$ it doesn't say which is $x$ and which is $y$ but it is conventional to write $x$ first and then $y$ so I am going to word my problem more carefully.

Verify that $(x, y) = (5, 7)$ is a solution to the equation in two variables $7x - 4y = 7.$

To solve this I substitute $x = 5$ and $y = 7$ into the left side of the equation and see if the value I obtain is equal to the right side. Substitution gives

$7x - 4y = 7 \times 5 - 4 \times 7 = 35 - 28 = 7.$

This is equal to the right side so $(x, y) = (5, 7)$ is a solution to $7x - 4y = 7.$

Let's try another pair of numbers.

Is $(x, y) = (6, 1)$ is a solution to the equation in two variables $7x - 4y = 7?$

Substitution this time yields

$7x - 4y = 7 \times 6 - 4 \times 1 = 42 - 4 = 38.$

The result is not equal to the right side of the equation $7x - 4y = 7$ and hence $(x, y) = (6, 1)$ is not a solution to the equation in two variables $7x - 4y = 7.$

I hope this helps,
Penny

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