solve the following simultaneous equation algebraically,for a and b
8a+5b=23
12a+3b=12
Here is one way. Subtract the second equation from the first.
-4a+2b=11
double it
-8a+4b=22
now add that to the first equation.
9b=45
b=5
Put that b into either equation and solve for a.
this is hard!!!!!
{4a+5b=23
To solve the simultaneous equations algebraically, we can use the method of substitution or elimination. Let's solve it using the method of substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation for a:
12a + 3b = 12
12a = 12 - 3b
a = (12 - 3b) / 12
Step 2: Substitute the expression obtained in Step 1 into the other equation.
Substituting a = (12 - 3b) / 12 in the first equation:
8a + 5b = 23
8((12 - 3b) / 12) + 5b = 23
Simplifying:
(96 - 24b) / 12 + 5b = 23
8 - 2b + 5b = 23
Combining like terms:
3b = 15
b = 5
Step 3: Substitute the value of b obtained in Step 2 back into one of the original equations to solve for a.
Using the first equation:
8a + 5(5) = 23
8a + 25 = 23
8a = 23 - 25
8a = -2
a = -2 / 8
a = -1/4
Therefore, the solution to the simultaneous equations is:
a = -1/4
b = 5