System of equations:
• Equation 1
[tex]5x-y=19[/tex]• Equation 2
[tex]y=2x-1[/tex]Procedure
To use the substitution method, we have to isolate one variable in one equation, and then replace the obtained expression in the other equation.
As y is already isolated in Equation 2, then we can replace the expression in terms of x in Equation 1 as follows:
[tex]5x-(2x-1)=19[/tex][tex]5x-2x+1=19[/tex][tex]3x=19-1[/tex][tex]3x=18[/tex][tex]x=\frac{18}{3}=6[/tex]As we now know the value of x, we can replace it in the isolated expression of y (Equation 2) and calculate the value of y:
[tex]y=2\cdot(6)-1[/tex][tex]y=12-1[/tex][tex]y=11[/tex]Answer: x = 6 and y = 11
