Elimination method in solving simultaneous equation, a+2b=13, 2a-3b=15
OMG, ur soooo mean
here
A+2B=13 2A-3B=5
clearly
if
a+2b=13
2a-3b=15
then multiply the first one by 2
2a+4b=26
2a-3b=15
-------------- subtract
0 + 7 b = 11
b = 11/7
now go back and get a
========================
if
A+2B=13
2A-3B=5
------------- multiply by 2 again
2A+4B=26
2A-3B=5
-----------------subtract again
7 b = 21
b = 3 much more reasonable
now go back and find a from either equation
I think we first eliminate the same coefficients and then change the signs
To solve the simultaneous equations using the elimination method, follow these steps:
Step 1: Align the equations so that the variables line up vertically.
a + 2b = 13
2a - 3b = 15
Step 2: Multiply one or both of the equations by a constant so that the coefficient of one variable in one equation is the same as the coefficient of the same variable in the other equation. In this case, we'll multiply the first equation by 2 and the second equation by 1 to make the coefficients of 'a' the same:
2(a + 2b) = 2(13)
2a + 4b = 26
1(2a - 3b) = 1(15)
2a - 3b = 15
Step 3: Since the coefficients of 'a' in both equations are now the same, we can subtract the second equation from the first equation to eliminate 'a'.
(2a + 4b) - (2a - 3b) = 26 - 15
2a - 2a + 4b + 3b = 11
7b = 11
Step 4: Solve for 'b' by dividing both sides of the equation by 7.
7b / 7 = 11 / 7
b = 11/7
Step 5: Substitute the value of 'b' back into one of the original equations to solve for 'a'. We can use the first equation for this.
a + 2(11/7) = 13
a + 22/7 = 13
Step 6: Solve for 'a' by subtracting 22/7 from both sides of the equation.
(a + 22/7) - 22/7 = 13 - 22/7
a = 13 - 22/7
Step 7: Simplify the expression on the right side of the equation.
a = (91 - 22) / 7
a = 69/7
Therefore, the solution to the simultaneous equations is a = 69/7 and b = 11/7.