Question

4x + 7y = -33

7x - 3y = 49


What is the solution for the system of equations above?

Answer 1

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.

First, let's multiply the second equation by 4 to make the coefficients of x equal:

28x - 12y = 196

Now, we can subtract this equation from the first equation to eliminate x:

(4x + 7y) - (28x - 12y) = -33 - 196

Combine like terms:

-24x + 19y = -229

Now, we have a new equation:

-24x + 19y = -229

Next, let's multiply the first equation by 3 to make the coefficients of y equal:

12x + 21y = -99

Now, we can subtract this equation from the second equation to eliminate y:

(7x - 3y) - (12x + 21y) = 49 - (-99)

Combine like terms:

-5x - 24y = 148

Now, we have a new equation:

-5x - 24y = 148

We now have a system of two equations:

-24x + 19y = -229
-5x - 24y = 148

Now, let's solve this system using the method of elimination.

First, let's multiply the second equation by -24 to make the coefficients of y equal:

120x + 576y = -3552

Now, we can add this equation to the first equation to eliminate y:

(-24x + 19y) + (120x + 576y) = -229 + (-3552)

Combine like terms:

96x + 595y = -3781

Now, we have a new equation:

96x + 595y = -3781

Finally, we can multiply the first equation by 595 and the second equation by 19 to make the coefficients of x equal:

-5656x - 4521y = 541395
-95x - 4560y = 2812

Now, we can add these equations to eliminate x:

(-5656x - 4521y) + (-95x - 4560y) = 541395 + 2812

Combine like terms:

-5751x - 9081y = 544207

Now, we have a new equation:

-5751x - 9081y = 544207

Now, we have a system of two equations:

96x + 595y = -3781
-5751x - 9081y = 544207

We can solve this system of equations using various methods, such as substitution or elimination. Let me know if you would like me to show you how to solve this system using a different method.