32x+36y+16=0
36x+32y+16=0
Find x and y
first of all, notice that each equation is divisible by 4
new equations:
8x + 9y = -4
9x + 8y = -4
multiply 1st by 8 ---> 64x + 72y = -32
multiply 2nd by 9 --> 81x + 72y = -36
subtract them
17x= -4
x = -4/17
into the 1st:8(-17/4) + 9y = -4
times 4
-136 + 36y = -16
36y = 120
y = 10/3
To find the values of x and y that satisfy the given equations, we can solve the system of equations using the method of elimination:
1) Multiply the first equation by 36 and the second equation by 32 to make the coefficients of x in both equations equal:
(36)(32x) + (36)(36y) + (36)(16) = 0
(32)(36x) + (32)(32y) + (32)(16) = 0
Simplifying:
1152x + 1296y + 576 = 0 (equation 1)
1152x + 1024y + 512 = 0 (equation 2)
2) Subtract equation 2 from equation 1 to eliminate x:
(1152x - 1152x) + (1296y - 1024y) + (576 - 512) = 0
Simplifying:
272y + 64 = 0
3) Solve for y:
272y = -64
y = -64/272
y = -4/17
4) Substitute the obtained value of y back into either equation to solve for x. Let's use equation 1 for this example:
1152x + 1296(-4/17) + 576 = 0
Simplifying:
1152x - 34848/17 + 576 = 0
1152x - 34848 + 9792/17 = 0
Combining like terms:
1152x - 25056/17 = 0
5) Solve for x:
1152x = 25056/17
x = (25056/17)/1152
x = 22/17
Therefore, the solution to the system of equations is x = 22/17 and y = -4/17.