Algebra worksheet (substitution ) online exercise for | Live ... - Free Printable

Let's solve each part of the Substitution Worksheet step by step.

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A. Evaluate each algebraic expression for the given value of the variables

#### 1) $ 6y - 5 $ for $ y = 7 $

Substitute $ y = 7 $:

$$
6(7) - 5 = 42 - 5 = \boxed{37}
$$

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#### 2) $ 4x^2 + 3x $ for $ x = 6 $

First, compute $ x^2 $:
$ 6^2 = 36 $

Now substitute:

$$
4(36) + 3(6) = 144 + 18 = \boxed{162}
$$

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#### 3) $ \frac{56}{x} + 3y $ for $ x = 4 $ and $ y = 3 $

Substitute values:

$$
\frac{56}{4} + 3(3) = 14 + 9 = \boxed{23}
$$

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#### 4) $ 4y^2 + 2y $ for $ y = 3 $

First, $ y^2 = 3^2 = 9 $

Now substitute:

$$
4(9) + 2(3) = 36 + 6 = \boxed{42}
$$

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B. For $ x = 3 $, $ y = 2 $, and $ c = -10 $, find:

#### 1) $ c^2 $

$$
(-10)^2 = (-10) \times (-10) = \boxed{100}
$$

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#### 2) $ (-x)^2 $

Here, $ x = 3 $, so $ -x = -3 $

$$
(-3)^2 = (-3) \times (-3) = \boxed{9}
$$

> Note: The square of a negative number is positive.

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#### 3) $ -x^2 $

This means negative of $ x^2 $, not $ (-x)^2 $. So we first square $ x $, then apply the negative sign.

$$
x^2 = 3^2 = 9 \Rightarrow -x^2 = -9
$$

So:
$$
\boxed{-9}
$$

> Important: $ -x^2 $ ≠ $ (-x)^2 $

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#### 4) $ \frac{c}{y} $

$ c = -10 $, $ y = 2 $

$$
\frac{-10}{2} = \boxed{-5}
$$

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#### 5) $ \sqrt{9y^2} $

First, $ y = 2 $, so $ y^2 = 4 $

Then:
$$
9y^2 = 9 \times 4 = 36
$$

$$
\sqrt{36} = \boxed{6}
$$

> Note: Square root gives the principal (non-negative) root.

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✔ Final Answers:

#### A:
1) $ 37 $
2) $ 162 $
3) $ 23 $
4) $ 42 $

#### B:
- $ c^2 = \boxed{100} $
- $ (-x)^2 = \boxed{9} $
- $ -x^2 = \boxed{-9} $
- $ \frac{c}{y} = \boxed{-5} $
- $ \sqrt{9y^2} = \boxed{6} $

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