Question Video: Finding the Unknown Coefficient in a Two-Variable Linear Equation given Its Solution Point | Nagwa Question Video: Finding the Unknown Coefficient in a Two-Variable Linear Equation given Its Solution Point | Nagwa

# Question Video: Finding the Unknown Coefficient in a Two-Variable Linear Equation given Its Solution Point Mathematics

Given that (4, 5) is a solution of 6𝑥 + 7𝑎𝑦 = 26, find 𝑎.

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### Video Transcript

Given that four, five is a solution of six 𝑥 plus seven 𝑎𝑦 equals 26, find 𝑎.

We are told in the question that the ordered pair four, five is a solution of the equation. This means that we can substitute 𝑥 equals four and 𝑦 equals five into the equation. This gives us six multiplied by four plus seven 𝑎 multiplied by five is equal to 26. Six multiplied by four is equal to 24. Seven multiplied by five is equal to 35. Therefore, seven 𝑎 multiplied by five is 35𝑎.

We can solve the equation 24 plus 35𝑎 equals 26 by firstly subtracting 24 from both sides. This gives us 35𝑎 is equal to two. Dividing both sides of this equation by 35 gives us a value of 𝑎 of two over 35 or two thirty-fifths. If the ordered pair four, five is a solution of six 𝑥 plus seven 𝑎𝑦 equals 26, then 𝑎 equals two over 35. We could check this answer by substituting our value of 𝑎 back in to the original equation.

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