To eliminate a variable, make its coefficients match. For 3x − 5y = −39 and 2x − 4y = −28, multiply the first by 2 and the second by 3 to get 6x in both. Subtracting removes x and leaves an equation in y.
Substitution is another method: rearrange one equation for one letter and put it into the other. Either way, find one unknown, then substitute to find the other, and check the pair in both equations.
Worked example
Solve 4x − 5y = −3 and −7x + 5y = 24
- Add the equations: −3x = 21, so x = −7.
- 4(−7) − 5y = −3 gives −5y = 25, so y = −5.
Answer:x = −7, y = −5
Key words
- elimination
- removing a variable by adding or subtracting equations
- substitution
- replacing a letter with an expression
- coefficient
- the number in front of a letter
Practise this
New questions every time.
Common Core-referenced: HSA-REI.C.6