{-4x+5y=27x−6y=-2

Question

What is the solution to the system of equations shown above?

f (-1,1/6)
g (5,-6)
h (-8,-1)
j (0,1/3)

Answer 1

To find the solution to this system of equations, we can solve it using any method we prefer, such as substitution or elimination.

Let's solve it using the elimination method. We will multiply the first equation by 2 and the second equation by 3 to eliminate the x term:

-8x + 10y = 54
27x - 18y = -6

Adding the two equations together, we get:

-8x + 10y + 27x - 18y = 54 - 6
19x - 8y = 48

Simplifying further, we have:

19x - 8y = 48

Now let's solve this equation for y:

-8y = 48 - 19x
y = (48 - 19x)/-8
y = (-48 + 19x)/8

Substituting this value of y into the first equation, we get:

-4x + 5((-48 + 19x)/8) = 27
-4x + (-240 + 95x)/8 = 27
-32x + (-240 + 95x) = 216
-32x - 240 + 95x = 216
63x - 240 = 216
63x = 456
x = 456/63
x = 8/3

Now substitute this value of x back into either equation to find y:

-4(8/3) + 5y = 27
-32/3 + 5y = 27
5y = 81 + 32/3
5y = 243/3 + 32/3
5y = 275/3
y = (275/3) / 5
y = 275/15
y = 55/3

So the solution to the system of equations is (8/3, 55/3).

None of the given options match this solution, so none of them is correct.