Question

Estimate the solution to the system of equations.7x - y = 7x + 2y = 6Choose 1 answer:

Answer 1

Write the equations

`\begin{gathered} 7x-y=7\ldots\text{.equation 1} \\ x+2y=6\ldots\text{Equation 2} \end{gathered}`

Using substitution method

Make x the subject of formula from equation 2

`\begin{gathered} x+2y=6 \\ Subtract\text{ 2y from both sides } \\ x+2y-2y=6-2y \\ \text{Then} \\ x=6-2y\ldots\text{equation 3} \end{gathered}`

Substitute the expression for x in equation 3 into equation 1

`\begin{gathered} 7x-y=7 \\ 7(6-2y)-y=7 \\ \text{Expand the paranthesis n} \\ 42-14y-y=7 \\ 42-15y=7 \\ \text{Subtract 42 from both sides } \\ 42-42-15y=7-42 \\ -15y=-37 \end{gathered}`

Then, divide both sides by -15 to obtain the value of

`\begin{gathered} -(15y)/(-15)=-(37)/(-15) \\ \text{Then} \\ y=(7)/(3)=2(1)/(3) \end{gathered}`

Finally, substitute the value of y into equation 3 to obtain x

`\begin{gathered} x=6-2y \\ \text{Put y=}\frac{\text{7}}{3} \\ x=6-2((7)/(3))=6-(14)/(3)=(18-14)/(3)=(4)/(3) \\ \text{Then } \\ x=1(1)/(3) \end{gathered}`

Therefore

Answer: x=1 1/3 and y=2 1/3

Option C