Question

Solve the system of equations. 4y + 11x – 67 = 0 2y + 5x - 19 = 0 x= y=​

Answer 1

`y=(136)/(9),\:x=(7)/(9)`

Explanation:

`\begin{bmatrix}4y+11x-67=2\\ y+5x-19=0\end{bmatrix}`

Isolate y for 4y+11x-67=2:

`y=(-11x+69)/(4)`

`\mathrm{Substitute\:}y=(-11x+69)/(4)`

`\begin{bmatrix}(-11x+69)/(4)+5x-19=0\end{bmatrix}`

`Simplify`

`\begin{bmatrix}(9x+69)/(4)-19=0\end{bmatrix}`

Isolate x for
`(9x+69)/(4)-19=0:`

`x=(7)/(9)`

`\mathrm{For\:}y=(-11x+69)/(4)`

`\mathrm{Substitute\:}x=(7)/(9)`

`y=(-11\cdot (7)/(9)+69)/(4)`

`(-11\cdot (7)/(9)+69)/(4)=(139)/(9)`

`y=(136)/(9)`

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`y=(136)/(9),\:x=(7)/(9)`

Answer 2

x = 29, y = -63

Explanation:

Solve the following system:

{4 y + 11 x - 67 = 0 | (equation 1)

{2 y + 5 x - 19 = 0 | (equation 2)

Express the system in standard form:

{11 x + 4 y = 67 | (equation 1)

v5 x + 2 y = 19 | (equation 2)

Subtract 5/11 × (equation 1) from equation 2:

{11 x + 4 y = 67 | (equation 1)

{0 x+(2 y)/11 = -126/11 | (equation 2)

Multiply equation 2 by 11/2:

{11 x + 4 y = 67 | (equation 1)

{0 x+y = -63 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{11 x+0 y = 319 | (equation 1)

{0 x+y = -63 | (equation 2)

Divide equation 1 by 11:

{x+0 y = 29 | (equation 1)

{0 x+y = -63 | (equation 2)

Collect results:

Answer: {x = 29, y = -63