Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Simultaneous equations - Equating coefficients.
Test Yourself 1.


 

Solve the following equations simultaneously by first equating the coefficients for one variable.

Note if we are given an equation with a variable having a coefficient of 1, we would simply revert to our previous technique.

Dont forget to test your set of solutions as you finish each pair by quickly substituting back into at least one of the original equations.

2x + 3y = 19

3x + 2y = 16

3x - 5y = 11

2x - 3y = 8

12y + 7z - 13 = 0

6y + z + 11 = 0

Hint.Here we only need to multiply Eqn 2 by 2 to equate the y coefficients. Less work!!!
Of course we could also have just rewritten equation 2 to be z = ... and then substituted. Numbers are getting a bit big but no real problem either way.
Go with your heart.

7a - 3h = 9

5a + 2h = 23

3m + 4n = -5

4m - 3n = 10

3c + 4d = 16

7c - 2d = 60

Hint.It is easier here to multiply Eqn 2 by 2 and leave Eqn 1 as it is.
The d coefficients are then +4 and -4. Then just add the equations. 

2m - 3n = 5

5m + 2n = -16

2x + 3y = 5

3x + 4y = 6

6x + 3y = 0

2x - 5y = 6