Simultaneous equations How to solve simultaneous equations using

Method 1 – Elimination method 6 x + y = 15 4 x +

Method 1 – Elimination method 3 x + 4 y = 17 x +

Method 1 – Elimination method 3 x +2 y = 18 2 x -

Method 2 – Substitution method 6 x + y = 15 4 x +

Elimination method How to solve simultaneous equations using the elimination method where both equations

Elimination method 4 x +3 y = 27 5 x - 2 y =

Elimination method 8 x + 6 y = 54 15 x - 6 y

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Simultaneous equations How to solve simultaneous equations using non-graphical methods.

Method 1 – Elimination method 6 x + y = 15 4 x + y = 11 2 x =4 x =2 6 x× 2 + y = 15 12 + y = 15 y =3 (1) (2) Step 1 – Number the equations Step 2 – Eliminate one of the unknowns Step 3 – Work out the unknown Step 4 – Using the value of x in equation 1 or 2 find the value of y.

Method 1 – Elimination method 3 x + 4 y = 17 x + 4 y = 3 2 x = 14 x =7 x 7 + 4 y = 3 4 y = -4 y = -1 (1) (2) Step 1 – Number the equations Step 2 – Eliminate one of the unknowns Step 3 – Work out the unknown Step 4 – Using the value of x in equation 1 or 2 find the value of y.

Method 1 – Elimination method 3 x +2 y = 18 2 x - y = 5 4 x -2 y = 10 7 x = 28 x =4 2 x× 4 - y = 5 8 -y= 5 (1) (2) (3) Step 1 – Number the equations Step 2 – Balance the coefficient of one of the unknowns Step 3 – Eliminate unknown by adding Step 4 – Using the value of x in equation 1 or 2 find the value of y. y= 3

Method 2 – Substitution method 6 x + y = 15 4 x + y = 11 (1) (2) y = 15 – 6 x 4 x +( y ) = 11 4 x – 6 x + 15 = 11 -2 x = -4 x =2 Step 1 – Number the equations Step 2 – Make one of the unknowns the subject of the formula in one of the equations. Step 3 – Substitute the value of the unknown into the other equation Step 4 – Calculate the value of the unknown

Method 2 – Substitution method 6 x + y = 15 4 x + y = 11 x =2 4 x× 2 + y = 11 8 + y = 11 y=3 (1) (2) Step 5 –Using the value of x in equation 1 or 2 find the value of y.

Elimination method How to solve simultaneous equations using the elimination method where both equations need to be changed to obtain the same coefficients in front of the unknown you wish to cancel

Elimination method 4 x +3 y = 27 5 x - 2 y = 5 8 x+6 y = 54 15 x - 6 y = 15 (1) (2) (3) (4) Step 1 – Number the equations Step 2 – Balance the coefficients of one of the unknowns in both the equations

Elimination method 8 x + 6 y = 54 15 x - 6 y = 15 23 x = 69 x =3 8 x× 3 + 6 y = 54 24 + 6 y = 54 6 y = 30 (3) (4) Step 3 – Eliminate one of the unknowns Step 4 – Work out the unknown Step 5 – Using the value of x in equation 1, 2, 3 or 4 find the value of y. y =5