4x + 8y = 4 and -2x - 7y = -11

Question

asked May 17, 2023 231k views

1 Answer

Sakthisundar · Answer 1 · 2023-05-20T19:56:01+0000

We have the following system of equations:

$\begin{gathered} 4x+8y=4 \\ -2x-7y=-11\ldots(A) \end{gathered}$

Solving by combining equations:

If we multiply equation A by 2, we get the following equivalent system:

$\begin{gathered} \\ 4x+8y=4\ldots(B) \\ -4x-14y=-22\ldots(C) \end{gathered}$

If we add both equation, we have

which gives

If we move the coefficient of y, we get

$\begin{gathered} y=(-18)/(-6) \\ y=3 \end{gathered}$

Finally, by substituting this result into equation B, we obtain

which leads to

If we move +24 to the right hand side,we get

$\begin{gathered} 4x=4-24 \\ 4x=-20 \end{gathered}$

and x is given by

$\begin{gathered} x=(-20)/(4) \\ x=-5 \end{gathered}$

Therefore, the answer is

$\begin{gathered} x=-5 \\ y=3 \end{gathered}$