Question

Solve the system of equations below.
6x+7y=5
5x+7y=3

Answer 1

You sure?

Answer 2

To solve this system of equations, we can use the method of substitution or elimination.

I will use the elimination method in this case.

First, we will multiply each term in the second equation by -6.

-6(5x+7y)= -6(3)
-30x - 42y = -18

Now, we will add the new equation to the first equation:

(6x + 7y) + (-30x - 42y) = 5 + (-18)
-24x - 35y = -13

Now we have a new equation: -24x - 35y = -13

To solve for x, we can rewrite one of the original equations in terms of y:

6x + 7y = 5
6x = 5 - 7y
x = (5 - 7y)/6

Now substitute x into the new equation:

-24((5 - 7y)/6) - 35y = -13
-24(5 - 7y) - 35*6y = -13*6
-120 + 168y - 210y = -78
-42y = -78 + 120
-42y = 42
y = 42/-42
y = -1

Now that we have y = -1, we can substitute this back into one of the original equations to solve for x:

6x + 7(-1) = 5
6x - 7 = 5
6x = 5 + 7
6x = 12
x = 12/6
x = 2

Therefore, the solution to the system of equations is x = 2, y = -1.

Answer 3

I apologize for the mistake. Let me recheck my calculations.

From our last substitution we know that y = -1.

Now we can substitute y = -1 back into one of the original equations to solve for x:

6x + 7y = 5
6x + 7(-1) = 5
6x - 7 = 5
6x = 12
x = 12/6
x = 2

Therefore, the correct solution to the system of equations is x = 2, y = -1. Thank you for pointing out the error.