Question

Solve the system of equations – 5x + y = 56 and x + y = -4 by combining the
equations.

Answer 1

x=-10; y=6

Explanation:

combine the equations:

-5x + y + x + y = 56 +(-4)

-4x + 2y = 52

add 4x to each side

2y=52+4x

divide by 2

y=26+2x

now substitute 26+2x for y in the second equation:

x + 26 + 2x = -4

3x + 26 = -4

3x = -30

x = -10

therefore y = 6

Answer 2

Your solution is (-10, 6).

Explanation:

Combining the equations is also known as substitution. This is done when you substitute one variable into another equation.

-5x + y = 56

x + y = -4

Let's change the second equation into one with one variable on each side.

y = -x - 4

Now, plug this into your first equation.

-5x + (-x - 4) = 56

Distribute the + sign.

-5x - x - 4 = 56

Combine the like terms.

-6x - 4 = 56

-6x = 60

Isolate x by dividing both sides by -6.

x = -10

Now plug this back into either equation.

-10 + y = -4

Add 10 to both sides to find y.

y = 6

Your solution is (-10, 6).

Check this by plugging in these values into the equation you have not checked yet.

-5(-10) + (6) = 56

50 + 6 = 56

56 = 56

Your solution is correct.

Hope this helps!