Question

Find the solution to the system of equations 5y = 1 + 6x and 6x + 4y = -10.

(1, 1)
(-1, -1)
(-1, 1)
(1, -1)

Answer 1

x = -1

y = -1

Explanation:

a) 5y=1 + 6x

b) 6x + 4y = - 10

a) ( 5y = 1 + 6x) = (y = 1/5 + 6/5x) = y = 6/5x + 1/5

b) 6x + 4(6/5x + 1/5) = -10 (substitution)

6x + 24/5x + 4/5 = - 10

54/5x + 4/5 = -10 (simplify)

54/5x = -10 - 4/5

54/5x = - 54/5

x = (- 54/5)/(54/5)

x = -1

a) 5y = 1 + (6)(-1). (Substitution)

y = 1 - 6

y = -5/5

y = -1

Answer 2

To find the solution to the system of equations:

1. 5y = 1 + 6x
2. 6x + 4y = -10

You can use the method of substitution or elimination. Let's use the elimination method to solve this system:

First, multiply equation 1 by 4 to make the coefficients of y in both equations equal:

1. 20y = 4 + 24x
2. 6x + 4y = -10

Now, subtract equation 2 from equation 1 to eliminate y:

(20y - 4y) = (4 + 24x) - (-10)

16y = 14 + 24x + 10

16y = 24x + 24

Now, divide both sides by 16 to solve for y:

y = (24x + 24) / 16
y = (3x + 3)

Now that we have the expression for y, we can substitute it back into one of the original equations to find the value of x. Let's use equation 2:

6x + 4y = -10

6x + 4(3x + 3) = -10

6x + 12x + 12 = -10

18x + 12 = -10

Subtract 12 from both sides:

18x = -10 - 12

18x = -22

Now, divide by 18 to solve for x:

x = -22 / 18
x = -11/9

So, the solution to the system of equations is (x, y) = (-11/9, 3x + 3). Now, let's find the values of x and y:

x = -11/9
y = 3x + 3
y = 3(-11/9) + 3
y = -11/3 + 3
y = (-11 + 9) / 3
y = -2 / 3

Therefore, the solution to the system of equations is (x, y) = (-11/9, -2/3). None of the provided options (1, 1), (-1, -1), (-1, 1), (1, -1) is the correct solution.