What you need to know

Things to remember:

• Substitution just means replacing a letter with a number.
• We don’t write $\times$ when there is a number before a letter, so you need to remember that it is hiding there!
• $xy=x\times y$
• A fraction is another way of writing a division question.

We have looked at substituting for a single variable before, so let’s have a quick look back at how we did that first.

Use substitution to find the value of $5x$ when $x = 13$

$$5x=5\times x=5\times13=65$$

Divisions questions could either appear as a division:

Use substitution to find the value of $x\div3$ when $x = 9$

$$x\div3=9\div3=3$$

Or as a fraction that we have to change:

Use substitution to find the value of $\frac{20}{x}$ when $x = 5$

$$\frac{20}{x}=20\div x=20\div5=4$$

When we are substituting for two variables we do it in the exact same way, we just have to substitute for two variables!

Use substitution to find the value of $x+y$ when $x = 13$ and $y = 11$

$$x+y=13+11=24$$

Use substitution to find the value of $x-y$ when $x = 4$ and $y = 9$

$$x-y=4-9=-5$$

Use substitution to find the value of $xy$ when $x = 13$ and $y = 12$

$$xy=x\times y=13\times 12= 156$$

Use substitution to find the value of $x\div y$ when $x = 72$ and $y = 9$

$$x\div y= 72\div9=8$$

Use substitution to find the value of $\frac{x}{y}$ when $x =64$ and $y = 8$

Hint: Remember, a fraction is just another way of writing a division.

$$\frac{x}{y}=x\div y= 64\div8=8$$

Example Questions

$$xy=x\times y=7\times 11= 77$$

$$\frac{y}{x}=y\div x= 35\div7=5$$