Substitution questions with answers

Questions

1. Question 1Positive whole numbers

   Given that $x = 6$ and $y = 5$, find the value of $x(y + 3)$.

   Show the worked solution

   1. Step 1: Substitute the values (negatives and fractions in brackets)$x(y + 3) = (6)(5 + 3)$
   2. Step 2: Work out the bracket first$= 6(8)$
   3. Step 3: Multiply$= 48$
2. Question 2Negative numbers, in brackets

   Given that $x = -6$ and $y = -6$, find the value of $2xy - 5$.

   Show the worked solution

   1. Step 1: Substitute the values (negatives and fractions in brackets)$2xy - 5 = 2\left(-6\right)\left(-6\right) - 5$
   2. Step 2: Work out each term$= 72 - 5$
   3. Step 3: Work out the answer$= 67$
3. Question 3Fractions

   Given that $x = \dfrac{2}{3}$ and $y = -2$, find the value of $x(y + 3)$.

   Show the worked solution

   1. Step 1: Substitute the values (negatives and fractions in brackets)$x(y + 3) = \left(\dfrac{2}{3}\right)(-2 + 3)$
   2. Step 2: Work out the bracket first$= \left(\dfrac{2}{3}\right)(1)$
   3. Step 3: Multiply$= \dfrac{2}{3}$
4. Question 4Algebraic fractions

   Given that $x = -3$ and $y = 3$, find the value of $\dfrac{3x + y}{x - y}$.

   Show the worked solution

   1. Step 1: Substitute the values (negatives and fractions in brackets)$\dfrac{3x + y}{x - y} = \dfrac{3\left(-3\right) + 3}{\left(-3\right) - 3}$
   2. Step 2: Work out the top and the bottom$= \dfrac{-6}{-6}$
   3. Step 3: Simplify the fraction$= 1$