Question

5x - y=19y=2x-1Slove the system by using the substitution method

Answer 1

System of equations:

• Equation 1

`5x-y=19`

• Equation 2

`y=2x-1`

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:

`5x-(2x-1)=19`
`5x-2x+1=19`
`3x=19-1`
`3x=18`
`x=(18)/(3)=6`

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:

`y=2\cdot(6)-1`
`y=12-1`
`y=11`

Answer: x = 6 and y = 11