Question

Choose the best method for solving and solve. Show your work.
y=-2x+17
y=8-x

Answer 1

x =
`-3`; y = 11

Explanation:

These two equations are linear simultaneous equations. They can be solved either by substitution, elimination or graphical method:

Substitution:

`y = 8 - x` ------- (equation i)

`y = 2x + 17` ---- (equation ii)

Substitute (equation i) into (equation ii):

`8 - x = 2x + 17`

Bring all the like terms together. In addition x has to be isolated and made the subject of the equation:

`8 - 17 = 2x + x`

`-9 = 3x`

x =
`-(9)/(3)`

∴ x =
`-3`

Substitute this value of x in any of the equations to solve for y:

`y = 8 - (-3)`

`y = 8 + 3`

∴ y = 11

This ordered pair of
`(-3, 11)` is a solution for both linear simultaneous equations. In addition, this particular pair is known as the 'point of intersection'.