Question

Graph the system of equations using technology. What is the x-coordinate of the solution? Round to the nearest hundredth.

2x-11y=4
3x-5y=14

Answer 1

The x - coordinate of the solution is
`x=5.83`

Step-by-step explanation:

The two equations are
`$2 x-11 y=4$` and
`$3 x-5 y=14$`

The image attached below shows the solution of the two equations.

The x - coordinate of the solution can be determined using substitution method.

Let us substitute
`$3 x-5 y=14$` ⇒
`y=-((14-3x))/(5)` in the equation
`$2 x-11 y=4$`

Thus, we have,

`2x-11(-((14-3 x))/(5))=4`

Simplifying, we get,

`2x+(154)/(5)-(33x)/(5) =4`

Adding the like terms, we have,

`-(23x)/(5) +(154)/(5) =4`

`(1)/(5) (-23x+154)=4`

Multiplying both sides by 5, we have,

`-23x+154=20`

`-23x=-134`

`x=5.826`

Rounding off to the nearest hundredth, we get,

`x=5.83`

Hence, the x - coordinate of the solution is
`x=5.83`