Question

6. Solve this system of linear equations without graphing:72 +lly = -27x + 3y = 30

Answer 1

SOLUTION

Write out the system of equation given

$\begin{gathered} 7x+11y=-2 \\ 7x+3y=30 \end{gathered}$

Using eliminationm method, we subtract the equation above to eliminate y

hence

$\begin{gathered} (7x-7x)+(11y-3y)=(-2-30) \\ 8y=-32 \end{gathered}$

Then divide both sides by 8, we have

$\begin{gathered} \frac{8y}{8}=-\frac{32}{8} \\ \text{Then} \\ y=-4 \end{gathered}$

Hence

y = -4

The substitute the value of y into any of the equation above to obtain x, we have

$\begin{gathered} \text{ Using the second equation, we have } \\ 7x+3y=30 \\ y=-4 \\ 7x+3(-4)=30 \\ 7x-12=30 \\ \end{gathered}$

Add 12 from both sides, we have

$\begin{gathered} 7x-12+12=30+12 \\ 7x=42 \\ \text{Divide both sides by 7, we have } \\ \frac{7x}{7}=\frac{42}{7} \\ \text{Then} \\ x=6 \end{gathered}$

Hence

x=6

Therefore

Answer is x = 6, y = - 4