Question

5x+7y=50 and 7x+5y=46 substitution method

Answer 1

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Answer 2

Answer:

The solution of the system of equations is (3,5).

Step-by-step explanation:

The given equations are

$5x+7y=50$              .... (1)

$7x+5y=46$              .... (2)

Substitute the value of y from equation (2) in equation (1).

$5y=46-7x$

$y=\frac{46-7x}{5}$                      .... (3)

Substitute this value in equation (1).

$5x+7(\frac{46-7x}{5})=50$  

$5x+\frac{322-49x}{5}=50$  

$\frac{25x+322-49x}{5}=50$  

$322-24x=250$  

$322-250=24x$  

$72=24x$  

$x=3$

The value of x is 3.

Substitute this value in equation (3).

$y=\frac{46-7(3)}{5}$

$y=\frac{46-21}{5}$

$y=\frac{25}{5}=5$

The value of y is 5.

Therefore the solution of the system of equations is (3,5).