Solve the simultaneous equations
5x + 2y = 11
4x - 3y = 18
Number the equations.
Make the y terms equal by multiplying all parts of equation (1) by 3 and all parts of equation (2) by 2.
This will give two 6y terms with different signs. The question could also be done by making the x terms equal by multiplying all parts of equation (1) by 4 and all parts of equation (2) by 5, and subtracting the equations.
The 6y terms have different signs, so they can be eliminated by adding equation (4) to equation (3).
Solve the equation to find x by dividing both sides by 23.
Substitute into either of the two original equations.
Solve this equation to find y.
Substitute x = 3 and y = - 2 into the other equation to check that they are correct
Solve the equations
x^{2} + y^{2} = 36
x = 2y + 6
Number the equations.
There is one quadratic equation and one linear equation so this must be done by substitution.
Equation (2) is equal to so this can be eliminated by substituting it into the part for equation (1).
Substitute into equation (1).
[1]
Expand the brackets, remember that a bracket squared should be treated the same as double brackets.
[1]
Simplify.
[1]
Rearrange to form a quadratic equation that is equal to zero.
The question does not give a specified degree of accuracy, so this can be factorised.
Take out the common factor of .
Solve to find the values of .
Let each factor be equal to 0 and solve.
[1]
Substitute the values of into one of the equations (the linear equation is easier) to find the values of .
[1]