Question Video: Evaluating Algebraic Expressions after Solving Linear Equations Mathematics

If (𝑥 + 21, 4) = (25, 𝑦 − 21), find √(𝑥 + 29𝑦).


Video Transcript

If 𝑥 plus 21, four is equal to 25, 𝑦 minus 21, find the square root of 𝑥 plus 29𝑦.

If the ordered pairs given are equal, their two components must be equal. 𝑥 plus 21 must equal 25, and four must equal 𝑦 minus 21. In order to solve the equation, 𝑥 plus 21 equals 25, we need to subtract 21 from both sides. This gives us a value of 𝑥 equal to four. When solving four is equal to 𝑦 minus 21, we need to add 21 to both sides. This gives us a value of 𝑦 equal to 25. We now need to substitute both of these values into the expression the square root of 𝑥 plus 29𝑦.

Using our order of operations, we need to multiply 29 by 25 then add four and finally square root this answer. 30 multiplied by 25 is equal to 750. This means that 29 multiplied by 25 is 725. We need to add four to 725. This is equal to 729. Square rooting is the opposite or inverse of squaring, and we know that 27 squared is equal to 729. This means that the square root of 729 is 27. This is the value of the square root of 𝑥 plus 29𝑦.

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