Question

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

Answer 1

Answer:

$y=\frac{136}{9},\:x=\frac{7}{9}$

Step-by-step explanation:

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

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

$y=\frac{-11x+69}{4}$

$\mathrm{Substitute\:}y=\frac{-11x+69}{4}$

$\begin{bmatrix}\frac{-11x+69}{4}+5x-19=0\end{bmatrix}$

$Simplify$

$\begin{bmatrix}\frac{9x+69}{4}-19=0\end{bmatrix}$

Isolate x for $\frac{9x+69}{4}-19=0:$

$x=\frac{7}{9}$

$\mathrm{For\:}y=\frac{-11x+69}{4}$

$\mathrm{Substitute\:}x=\frac{7}{9}$

$y=\frac{-11\cdot \frac{7}{9}+69}{4}$

$\frac{-11\cdot \frac{7}{9}+69}{4}=\frac{139}{9}$

$y=\frac{136}{9}$

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

$y=\frac{136}{9},\:x=\frac{7}{9}$

Answer 2

Answer:

x = 29, y = -63

Step-by-step 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