Question

Solve the system of equations below using substitution4x – 6y = 303x + 7y = 80

Answer 1

The system of equation is given below as

`\begin{gathered} 4x-6y=30-------(1) \\ 3x+7y=80-------(2) \end{gathered}`

Step 1:

From equation (1), make x the subject of the formula

`\begin{gathered} 4x-6y=30 \\ 4x=30+6y \\ (4x)/(4)=(30)/(4)+(6y)/(4) \\ x=(30)/(4)+(6y)/(4)-------(3) \end{gathered}`

Step 2:

Substitute equation (3) in equation (2)

`\begin{gathered} 3x+7y=80 \\ 3((30)/(4)+(6y)/(4))+7y=80 \\ (90)/(4)+(18y)/(4)+7y=80 \\ multiply\text{ through by 4} \\ 4((90)/(4))+4((18y)/(4))+4(7y)=4(80) \\ 90+18y+28y=320 \\ 46y+90=320 \\ 46y=320-90 \\ 46y=230 \\ (46y)/(46)=(230)/(46) \\ y=5 \end{gathered}`

Step 3:

Substitute y=5 in equation (3)

`\begin{gathered} x=(30)/(4)+(6y)/(4) \\ x=(30)/(4)+6((5)/(4)) \\ x=(30)/(4)+(30)/(4) \\ x=(60)/(4) \\ x=15 \end{gathered}`

Hence,

The solution to the system of equations is

`\Rightarrow x=15,y=5`