Solve the following simultaneous equation:
8x+3y=23
6x+5y=9
follow the method I showed you in
http://www.jiskha.com/display.cgi?id=1268685141
first one by 5, second one by 3, subtract them etc.
To solve this simultaneous equation, we can use either the substitution method or the elimination method. I will explain the process using the elimination method:
Step 1: Multiply both sides of the first equation by 5 and the second equation by 3 to make the coefficients of the y terms the same:
(1st equation) 5 * (8x + 3y) = 5 * 23
(2nd equation) 3 * (6x + 5y) = 3 * 9
Simplifying, we get:
40x + 15y = 115
18x + 15y = 27
Step 2: Subtract the second equation from the first equation to eliminate the y term:
(1st equation) - (2nd equation):
(40x + 15y) - (18x + 15y) = 115 - 27
Simplifying, we get:
22x = 88
Step 3: Divide both sides of the equation by 22 to solve for x:
22x / 22 = 88 / 22
x = 4
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
8x + 3y = 23
8(4) + 3y = 23
32 + 3y = 23
Step 5: Solve for y by subtracting 32 from both sides:
3y = 23 - 32
3y = -9
Step 6: Divide both sides by 3 to get the value of y:
3y / 3 = -9 / 3
y = -3
So, the solution to the simultaneous equations is x = 4 and y = -3.