Solution:
Consider the following linear system of equations:
Equation 1:[tex]y\text{ = 6x -1 }[/tex]From equation 1, we can replace y= 6x-1 into equation 2 to obtain:
[tex]3x+2(6x-1)\text{ = 43}[/tex]this is equivalent to:
[tex]3x\text{ + 12x - 2 = 43}[/tex]putting together similar terms, we get:
[tex]3x\text{ + 12x = 43 +2}[/tex]this is equivalent to:
[tex]15x\text{ = 45}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{45}{15}=\text{ 3}[/tex]replacing this value (x=3) into equation 1, we can get the value of y:
[tex]y\text{ = 6(3)-1 = 18-1 = 17}[/tex]then, we can conclude that the solution of this system of equations is:
[tex](x,y)\text{ = (3,17)}[/tex]