3a+9b=8b-a 5a-10b=4a-9b+5
What does a and b equal?
Please check your answer below.
Yes, scroll down.
To find the values of a and b, we can solve the given system of equations using either the substitution method or the elimination method. Let's use the elimination method in this case.
Given equations:
3a + 9b = 8b - a ---(1)
5a - 10b = 4a - 9b + 5 ---(2)
Step 1: Multiply equation (1) by -1 to change the signs of the terms involving 'a':
-3a - 9b = -8b + a
Step 2: Add the modified equation (1) to equation (2) to eliminate the 'a' terms:
-3a - 9b + 5a - 10b = -8b + a + 4a - 9b + 5
2a - 19b = -4b + 5 ---(3)
Step 3: Simplify equation (3):
2a - 19b + 4b = 5
2a - 15b = 5 ---(4)
Step 4: Multiply equation (2) by 2 to make the coefficients of 'a' in equations (2) and (4) equal:
10a - 20b = 8a - 18b + 10 ---(5)
Step 5: Simplify equation (5):
10a - 8a - 20b + 18b = 10
2a - 2b = 10 ---(6)
Step 6: Solve equations (4) and (6) as a system:
2a - 15b = 5 ---(4)
2a - 2b = 10 ---(6)
Step 7: Subtract equation (4) from (6) to eliminate 'a':
2a - 2b - (2a - 15b) = 10 - 5
2a - 2b - 2a + 15b = 5
13b = 5
Step 8: Solve for 'b':
b = 5 / 13
Step 9: Substitute the value of 'b' back into equation (4) to solve for 'a':
2a - 15(5 / 13) = 5
2a - 75 / 13 = 5
2a = 5 + 75 / 13
2a = (65 + 75) / 13
2a = 140 / 13
a = (140 / 13) / 2
a = 70 / 13
Therefore, the values of a and b are a = 70/13 and b = 5/13, respectively.