Question

How do I solve for x and y in these two linear equations? -4x-7y=5; -3x+2y=11.

Answer 1

\(\normalsize\color{green}{ -4x-7y=5\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ -3x+2y=11\LARGE\color{white}{ \rm │ }}\)
multiply the 1st equation times 3, and multiply the second equation times -4, \(\normalsize\color{green}{\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ -12x-21y=15\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ 12x-8y=-44\LARGE\color{white}{ \rm │ }}\) Now, add them together

\(\Huge\color{green}{ \bf \text{_______________} }\)
You get \(\normalsize\color{green}{ 0x-29y=-29\LARGE\color{white}{ \rm │ }}\), and this simplifies to,
\(\normalsize\color{green}{ 29y=-29\LARGE\color{white}{ \rm │ }}\) and therefore, \(\normalsize\color{green}{ y=1.\LARGE\color{white}{ \rm │ }}\)

Answer 2

Once you know the y,

\(\normalsize\color{green}{ -4x-7y=5\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ -3x+2y=11\LARGE\color{white}{ \rm │ }}\)

─────────────
\(\normalsize\color{green}{ -4x-7(1)=5\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ -3x+2(1)=11\LARGE\color{white}{ \rm │ }}\)

─────────────
\(\normalsize\color{green}{ -4x-7=5\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ -3x+2=11\LARGE\color{white}{ \rm │ }}\)

─────────────
\(\normalsize\color{green}{ -4x=12\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ -3x=9\LARGE\color{white}{ \rm │ }}\)

─────────────
\(\normalsize\color{green}{ x=-3\LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ x=-3\LARGE\color{white}{ \rm │ }}\)

Answer 3

I  not  only  solved  for  x,  but  also  checked,  and verified that when the solution to the system is \(\normalsize\color{green}{ (-3,1)\LARGE\color{white}{ \rm │ }}\) .

Answer 4

Next time, please try to post this question in mathematics, because this section (where you posted it) is a FEEDBACK section.

\(\LARGE\color{blue}{\bf {you~~~can~~~find~~~any~~~section~~~by:} }\)
\(\large \color{black}{\rm { 1) } }\) clicking "more subjects" (the top left corner, towards the center)
\(\large \color{black}{\rm { 2) } }\) typing in the name of the section (name of a section can be "history" Mathematics and other section for each unique area of studying).