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
Answer:
[tex]y=\frac{136}{9},\:x=\frac{7}{9}[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}4y+11x-67=2\\ y+5x-19=0\end{bmatrix}[/tex]
Isolate y for 4y+11x-67=2:
[tex]y=\frac{-11x+69}{4}[/tex]
[tex]\mathrm{Substitute\:}y=\frac{-11x+69}{4}[/tex]
[tex]\begin{bmatrix}\frac{-11x+69}{4}+5x-19=0\end{bmatrix}[/tex]
[tex]Simplify[/tex]
[tex]\begin{bmatrix}\frac{9x+69}{4}-19=0\end{bmatrix}[/tex]
Isolate x for [tex]\frac{9x+69}{4}-19=0:[/tex]
[tex]x=\frac{7}{9}[/tex]
[tex]\mathrm{For\:}y=\frac{-11x+69}{4}[/tex]
[tex]\mathrm{Substitute\:}x=\frac{7}{9}[/tex]
[tex]y=\frac{-11\cdot \frac{7}{9}+69}{4}[/tex]
[tex]\frac{-11\cdot \frac{7}{9}+69}{4}=\frac{139}{9}[/tex]
[tex]y=\frac{136}{9}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=\frac{136}{9},\:x=\frac{7}{9}[/tex]
