The same pair of values must satisfy both equations.
For elimination, multiply every term of an equation by the same number. For substitution, replace a variable by an equal expression.
Substitute the final pair into both original equations to check.
Example 1
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 6.Multiply every term of (1) by 3.Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Example 2
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 12.Multiply every term of (1) by 4.Multiply every term of (2) by 3. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Your turn
Question 1
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Check answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 20.Multiply every term of (1) by 5.Multiply every term of (2) by 4. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Question 2
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Check answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 6.Multiply every term of (1) by 3.Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Question 3
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Check answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 12.Multiply every term of (1) by 4.Multiply every term of (2) by 3. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Question 4
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Check answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 20.Multiply every term of (1) by 5.Multiply every term of (2) by 4. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Question 5
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Check answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 6.Multiply every term of (1) by 3.Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 20.Multiply every term of (1) by 5.Multiply every term of (2) by 4. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 6.Multiply every term of (1) by 3.Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 12.Multiply every term of (1) by 4.Multiply every term of (2) by 3. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 20.Multiply every term of (1) by 5.Multiply every term of (2) by 4. Subtract the new second equation from the new first equation to eliminate .
Substitute into (1).
Solve the simultaneous equations.
Read the x- and y-coordinates where the two lines intersect. Check by substitution.Answer
Label this equation (1).Label this equation (2). Match the coefficients of using their lowest common multiple, 6.Multiply every term of (1) by 3.Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate .