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What is the value of x and y

76x + 49y = 474.25

54x + 37y = 346.25

Guest Nov 28, 2017
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#1
+18777
+2

What is the value of x and y

76x + 49y = 474.25

54x + 37y = 346.25

$$\begin{array}{|rcl|rcl|} \hline x&=& \displaystyle \dfrac{ \begin{vmatrix} 474.25 & 49 \\ 346.25 & 37 \end{vmatrix} } { \begin{vmatrix} 76 & 49 \\ 54 & 37 \end{vmatrix} } \quad & \quad y&=& \displaystyle \dfrac{ \begin{vmatrix} 76 & 474.25 \\ 54 & 346.25 \end{vmatrix} } { \begin{vmatrix} 76 & 49 \\ 54 & 37 \end{vmatrix} } \\\\ x&=& \displaystyle \dfrac{474.25\cdot 37-346.25\cdot 49} { 76\cdot 37-54\cdot 49 } \quad & \quad y&=& \displaystyle \dfrac{ 76\cdot 346.25- 54\cdot 474.25 } { 76\cdot 37-54\cdot 49 } \\\\ x&=& \displaystyle \dfrac{581} { 166 } \quad & \quad y&=& \displaystyle \dfrac{705.5} { 166 } \\\\ x&=& \displaystyle 3.5 \quad & \quad y&=& \displaystyle 4.25 \\ \hline \end{array}$$

heureka  Nov 28, 2017
#2
+2

Solve the following system:
{76 x + 49 y = 474.25 | (equation 1)
54 x + 37 y = 346.25 | (equation 2)

Subtract 27/38 × (equation 1) from equation 2:
{76 x + 49 y = 474.25 | (equation 1)
0 x+(83 y)/38 = 9.28289 | (equation 2)

Multiply equation 2 by 38/83:
{76 x + 49 y = 474.25 | (equation 1)
0 x+y = 4.25 | (equation 2)

Subtract 49 × (equation 2) from equation 1:
{76 x+0 y = 266. | (equation 1)
0 x+y = 4.25 | (equation 2)

Divide equation 1 by 76:
{x+0 y = 3.5 | (equation 1)
0 x+y = 4.25 | (equation 2)

x = 3.5
y = 4.25

Guest Nov 28, 2017

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