Question

Solve the system of equations 4x+5y=-14 and -5x-8y=10 by combining the equations.

Answer 1

The solution of the system is:

x = 62/7

y = 30/7

How to solve the system of equations?

Here we have the system:

4x + 5y = -14

-5x - 8y = 10

To solve it by combining the equations, we need to try to remove one of the variables.

If we take the sum of 5 times the first equation and 4 times the second equation we get:

5*(4x + 5y) + 4*(-5x - 8y) = 5*(-14) + 4*10

If we simplify that we get:

20x  + 25y - 20x - 32y = -30

-7y = -30

Now we can solve that for y:

y = -30/-7 = 30/7

Now to get the value of x, we can replace the value of y in any of the given equations:

Using the first one:

4x + 5y = -14

x = (-14 - 5y)/4

x = (-14 - 5*30/7)/4 = (-98/7 - 150/7)/4 = 248/28 = 124/14 = 62/7

The solution of the system is:

x = 62/7

y = 30/7

If you want to learn more about systems of equations:

brainly.com/question/13729904

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