Much work in mathematics requires us to substitute values into an algebraic expression. This is especially true when using formulas to calculate quantities such as area and volume. It really isn't difficult, but as with anything it can be a tad confusing until you get the hang of it. Look at the examples below that show how to substitute values into some different algebraic expressions.
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Consider the following problem: Evaluate the algebraic expression x + 2y for x = 3 and y = 4. This just means to rewrite the expression but substitute the number 3 for the x and the number 4 for the y, then do the computation. It looks like this:
x + 2y 3 + 2(4) 3 + 8 = 11 So the algebraic expression x + 2y, when evaluated for x = 3 and y = 4, equals 11.
Look at another example. Substitute 2 for x and 5 for y in the algebraic expression 4x - 3y. Just as we did in Step 1, rewrite the expression, substitute the numerical values for x and y, and do the computation. Here it is: 4x - 3y 4(2) - 3(5) 8 - 15 = -7 The algebraic expression 4x - 3y evaluated for x = 2 and y = 5 equals -7.
Look at the formula that represents the volume of a rectangular solid. The formula is V = l x w x h, where l represents the length, w represents the width, and h represents the height. Suppose we want to use the formula to find the volume of a rectangular box that is 3 feet long, 2 feet wide, and 1 foot high. Re-write the volume formula and substitute the corresponding number values in for l, w, and h. V = l x w x h V = 3 x 2 x 1 V = 6 And since our units are in feet, we will write the volume as 6 cubic feet.
Review a more complicated expression. Consider 3x² + 4x - 2xy + y² + 5z, evaluated for x = 2, y = 3, and z = 4. Here's how it looks: 3x² + 4x - 2xy + y² + 5z 3(2)² + 4(2) - 2(2)(3) + (3)² + 5(4) 3(4) + 8 - 12 + 9 + 20 12 + 8 - 12 + 9 + 20 = 37
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