Question

Determine the solution to the system of linear equations given below. Ay y = -x + 3 -2 01 2 X B YF X2 0.00 0:26 1x

Answer 1

The solution is the intersection point of the 2 lines.

The given two equations are:

`\begin{gathered} y=-(2)/(3)x+3 \\ \text{and} \\ y=(3)/(2)x-2 \end{gathered}`

Equating both equations, we can solve for x:

`\begin{gathered} -(2)/(3)x+3=(3)/(2)x-2 \\ 3+2=(3)/(2)x+(2)/(3)x \\ 5=(13)/(6)x \\ x=(5)/((13)/(6)) \\ x=5*(6)/(13) \\ x=(30)/(13) \end{gathered}`

Substituting this value into the second equation, we can find y:

`\begin{gathered} y=(3)/(2)x-2 \\ y=(3)/(2)((30)/(13))-2 \\ y=(90)/(26)-2 \\ y=(45)/(13)-(26)/(13) \\ y=(19)/(13) \end{gathered}`

The solution set or intersecting point is:

`(x,y)=((30)/(13),(19)/(13))`

Converting to decimal and rounding we can say:

(x, y) = (2.3, 1.5)