How to solve
5d=2e-14
5e=d+12. Using elimination method
If you insist on elimination.... (substitution would be easy)
first arrange them in proper form:
2e - 5d = 14
5e - d = 12
multiply the 2nd by 5, leave the first one alone
2e - 5d = 14
25e - 5d = 60
now subtract the 1st from the 2nd
23e = 46
e = 2
sub that back into the original 1st
5d = 2(2) - 14
5d = -10
d = -2
To solve the system of equations using the elimination method, we need to eliminate one variable by manipulating the equations.
Given:
1) 5d = 2e - 14
2) 5e = d + 12
Let's eliminate the variable 'd' from the equations:
Step 1: Multiply equation (2) by 5 to make the coefficients of 'd' the same.
5(5e) = 5(d + 12)
25e = 5d + 60
Step 2: We now have two equations with the same coefficient for 'd'. Now, we can subtract equation (1) from equation (2) to eliminate 'd'.
(25e - 5d) - (5d) = (5d + 60) - (2e - 14)
25e - 5d - 5d = 5d + 60 - 2e + 14
25e - 10d = 5d + 74 - 2e
Simplifying the equation further:
25e - 10d = 5d + 74 - 2e
25e + 2e = 5d + 10d + 74
27e = 15d + 74
Step 3: Now, we have one equation in terms of 'd' and 'e'. Let's solve it further to find the values of 'd' and 'e'.
Given: 5e = d + 12
Substitute the value of 'd' from the equations (2) into equation (3):
27e = 15(5e - 12) + 74
Expanding and solving:
27e = 75e - 180 + 74
27e - 75e = -106
-48e = -106
e = (-106) / (-48)
e = 2.2083 (rounded to 4 decimal places)
Step 4: Substitute the value of 'e' from equation (4) into equation (2) to find the value of 'd':
5e = d + 12
5(2.2083) = d + 12
11.0415 = d + 12
d = 11.0415 - 12
d = -0.9585 (rounded to 4 decimal places)
Therefore, the solution to the system of equations is:
d ≈ -0.9585
e ≈ 2.2083
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Write down the two equations:
5d = 2e - 14 ...(Equation 1)
5e = d + 12 ...(Equation 2)
Step 2: Multiply both sides of Equation 2 by 5 to make the coefficient of d the same as Equation 1:
25e = 5d + 60 ...(Equation 3)
Step 3: Notice that the left side of Equation 3 is the same as the left side of Equation 1. Therefore, you can subtract Equation 3 from Equation 1 to eliminate the d variable:
(5d - 5d) = (2e - 14) - (5d + 60)
0 = -3d - 74
Step 4: Simplify the equation:
-3d = -74
Step 5: Multiply both sides of the equation by -1/3 to solve for d:
-3d * (-1/3) = -74 * (-1/3)
d = 74/3
Step 6: Substitute the value of d back into Equation 2 to solve for e:
5e = (74/3) + 12
Step 7: Simplify the equation:
5e = (74 + 36)/3
5e = 110/3
Step 8: Divide both sides of the equation by 5 to solve for e:
e = (110/3) * (1/5)
e = 22/3
So, the solution to the system of equations is: d = 74/3 and e = 22/3.