Question

Find the co-ordinates of the point of intersection of the two lines (equations of the lines are given below).

2x - 7y = 2
4x + 5y = 42

Hint: solve by elimination

Answer 1

The coordinates of the point of intersection of the two lines is
`(8,2)`

Step-by-step explanation:

The two equations are
`$2 x-7 y=2$` and
`$4 x+5 y=42$`

To determine the point of intersection of the two lines, we shall the equations using elimination method.

Thus, multiplying the equation
`$2 x-7 y=2$` by -2, we have,

`\begin{aligned}-4 x+14 y &=-4 \\ 4 x+5 y &=42 \end{aligned}$\\---------------------------\\`

`19y=38`

`y=2`

Substituting
`y=2` in the equation
`$2 x-7 y=2$`, we get,

`2x-7(2)=2`

`2x-14=2`

Adding both sides by 14, we get,

`2x=16`

Dividing both sides by 2, we get,

`x=8`

Thus, the coordinates of the point of intersection of the two lines is
`(8,2)`