Linear Equations in Two Variables Worksheets

Using this page

Practise equations such as 2x + 3y = 12. Find y when x is given, or check whether a pair such as (3, 2) is a solution by putting its numbers into the equation. Switch on negative numbers for harder sheets. Linear equations in two variables are part of Class 9 maths in India (NCERT) and the Year 8 to Year 9 algebra strand in Australia.

Tips

• Show the working, even when the answer seems obvious; it makes mistakes easy to spot.
• Check each answer: put it back into an equation, or estimate before working out.
• Start with the easier setting and move up once most answers are right.
• Mix one older sheet into each week so earlier skills stay fresh.

Worked example

2x + 3y = 12 when x = 3. Put x = 3: 2 × 3 + 3y = 12, so 6 + 3y = 12 and 3y = 6, so y = 2. The pair (3, 2) is a solution. Check: 2 × 3 + 3 × 2 = 6 + 6 = 12.

Common mistakes

Putting the numbers in the wrong places and swapping x and y.

Forgetting that a pair must make the equation true. One correct number is not enough.

How to use this generator

Choose the options above the sheet: the number of questions and the settings for this kind of worksheet. Every change makes a new sheet straight away, and New worksheet gives a different set of questions with the same settings.

Each sheet has a worksheet number printed at the top. Type the same number later, or keep the page link, to print exactly the same questions and answer key again. Leave Answer key page ticked to print the answers on a second page, then press Print. Every printed page carries the makekite logo and web address.

Common questions

Why are there so many solutions?
An equation in two variables has infinitely many solutions, and they lie on a straight line when drawn on a graph. These sheets look at single solutions.

Can I make the sheet harder?
Yes. Use the options above the sheet: more digits, a harder level, brackets or negative numbers where they are offered.

Can I print the same worksheet again?
Yes. Note the worksheet number printed at the top, or keep the link in your browser's address bar, which ends with that number. Entering it later gives the same questions and answers.

Is it free?
Yes. There is no sign-up, and nothing you choose is sent anywhere: the sheets are made in your browser.