Substitution and evaluating expressions
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Substitution and evaluating expressions
Video transcript
Now, let's think about expressions with more than one variable. So say I had the expression a plus-- I'll do a really simple one, a plus b. And I want to evaluate this expression when a is equal to 7 and b is equal to 2. And I encourage you to pause this and try this on your own. Well, wherever we see the a, we would just replace it with the 7. And wherever we see the b, we'd replace it with the 2. So when a equals 7 and b equals 2, this expression will be 7 plus 2, which, of course, is equal to 9. So this expression would be equal to 9 in this circumstance. Let's do a slightly more complicated one. Let's say we have the expression x times y minus y plus x. Actually, let's make it plus 3x. Or another way of saying it plus 3 times x. So let's evaluate this when x is equal to 3 and y is equal to 2. And once again, I encourage you to pause this video and try this on your own. Well, everywhere we see an x, let's replace it with a 3. Every place we see a y, let's replace it with a 2. So this is going to be equal to 3 times y. And y is 2 in this case. 3 times 2 minus 2 plus this 3 times x. But x is also now equal to 3. So what is this going to be equal to? Well, this is going to be equal to 3 times 2 is 6. This 3 times 3 is 9. So it simplifies to 6 minus 2, which is 4, plus 9, which is equal to 13. So in this case, it is equal to 13.
Video transcript
A local hospital is holding a raffle as a fundraiser. The individual cost of participating in the raffle is given by the following expression-- 5t plus 3, or 5 times t plus 3, where t represents the number of tickets someone purchases. Evaluate the expression when t is equal to 1, t is equal to 8, and t is equal to 10. So let's first take the situation where t is equal to 1. Then this expression right over here becomes-- and I'll use that same color-- becomes 5 times 1. 5 times 1 plus 3. 5 times 1 plus 3, and we know from order of operations, you do the multiplication before you do the addition. So this will be 5 times 1 is 5 plus 3, and then this is clearly equal to 8. Now let's do it when t is equal to 8. So when t is equal to 8, this expression becomes-- and I'll do the same colors again-- 5 times 8 plus 3. Same color of green. And once again, 5 times 8 is 40, and then we have the plus 3, there so this is equal to 43. And so we have the last situation, with t is equal to 10. I'll do that in blue. So we have 5 times 10. So 5t is 5 times 10. Instead of a t, put a 10 there. 5 times 10 plus 3. That's a slightly different shade of green, but I think you get the idea. 5 times 10 is 50. We do 50, and then we're going to have to add 3 to that, and that is equal to 53. And we're done.
A variable is a letter, for example x, y or z, that represents an unspecified number.
$$6+x=12$$
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Example
Calculate the following expression for x=3 and z=2
$$6z+4x=\: ?$$
Solution: Replace x with 3 and z with 2 to evaluate the expression.
$$6z+4x=\: ?$$
$$6\cdot {\color{blue} 2}+ 4\cdot {\color{blue} 3}=?$$
$$\: \, 12+12=24$$
Video lesson
Evaluate the following expression for x = 2, y = 5 and z = 4
$$4x+(7-z)-6y$$