3 days ago

Find the values of x1 and x2 where the following two constraints intersect.

Mathematics

1 answer:

Inessa [9K]3 days ago

4 0

Answer: x1 = 251/26, x2 = -111/26

Step-by-step explanation:

Greetings!

As illustrated in the diagram, the point you seek is where the two lines intersect.

This intersection point is found by solving the system of linear equations (both equations must be satisfied by the point):

$9x_1 +7x_2=57\\4x_1 + 6x_2 = 13$

You can approach solving it using the substitution method:

$\text{solve for x1 in the first equation:}\\x_1 = \frac{1}{9}(57 - 7x_2)$

Then substitute x1 into equation 2 to resolve x2:

$\frac{4}{9}(57-7x_2) + 6x_2 = 13\\\text{doing the algebra you get:}\\x_2 = \frac{-111}{26}$

After which, utilize the x2 value to establish x1:

$x_1 = \frac{1}{9}(57 - 7x_2)= \frac{1}{9}(57 + 7*\frac{111}{26}) = 251/26\\$

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