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 $x=5.83$

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 $3 x-5 y=14$ ⇒ $y=-\frac{(14-3x)}{5}$ in the equation $2 x-11 y=4$

Thus, we have,

$2x-11(-\frac{(14-3 x)}{5})=4$

Simplifying, we get,

$2x+\frac{154}{5}-\frac{33x}{5} =4$

Adding the like terms, we have,

    $-\frac{23x}{5} +\frac{154}{5} =4$

$\frac{1}{5} (-23x+154)=4$

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 $x=5.83$