Question

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

Answer 1

SOLUTION

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

$\begin{gathered} -\frac{15y}{-15}=-\frac{37}{-15} \\ \text{Then} \\ y=\frac{7}{3}=2\frac{1}{3} \end{gathered}$

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

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

Therefore

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

Option C