8y=7+14x
18y-2=-7x
I will assume you are solving.
8y=7+14x ---> 14x - 8y = -7
18y-2=-7x --> 7x + 18y = 2
I suggest multiplying the 2nd by 2, then subtracting them.
That will eliminate the x's , then solve for y.
You know what to do next.
To solve the equations 8y = 7 + 14x and 18y - 2 = -7x, we can use the method of substitution. First, let's solve the first equation for y.
1) 8y = 7 + 14x
To isolate y, we divide both sides of the equation by 8:
8y/8 = (7 + 14x)/8
y = (7 + 14x)/8
Now that we have the expression for y in terms of x, we can substitute it into the second equation.
2) 18y - 2 = -7x
Substitute y with (7 + 14x)/8:
18((7 + 14x)/8) - 2 = -7x
Next, simplify the equation:
(18/8)(7 + 14x) - 2 = -7x
Simplify further:
(9/4)(7 + 14x) - 2 = -7x
Distribute 9/4 to both terms inside the parentheses:
(63/4 + (9/4)(14x)) - 2 = -7x
Simplify:
63/4 + (9/4)(14x) - 2 = -7x
Combine like terms:
63/4 + (126/4)x - 2 = -7x
Now, let's get all the x terms on one side of the equation:
(126/4)x + 7x = 63/4 + 2
Simplify:
(126/4 + 28/4)x = 63/4 + 8/4
Combine the fractions:
(154/4)x = 71/4
To get x by itself, divide both sides of the equation by 154/4:
x = (71/4) / (154/4)
Simplify the division:
x = 71/154
Now that we have the value of x, we can substitute it back into the first equation to find y.
y = (7 + 14(71/154))/8
Simplify the expression:
y = (7 + (994/77))/8
Simplify further:
y = (77*7/77 + 994/77) / 8
Combine the fractions:
y = (539/77 + 994/77) / 8
Simplify:
y = (1533/77) / 8
To divide fractions, multiply the numerator by the reciprocal of the denominator:
y = (1533/77) * (1/8)
Simplify:
y = 1533/616
Therefore, the solution to the system of equations is x = 71/154 and y = 1533/616.