I don't know how to solve this by elimination 4c - 3d=1 2c + 4d=17
4 c - 3 d = 1 , 2 c + 4 d = 17
Multiply the second equation by 2.
4 c + 8 d = 34
Now:
4 c - 3 d = 1
-
4 c + 8 d = 34
_____________
4 c - 4 c - 3 d - 8 d = 1 - 34
- 11 d = - 33
Divide both sides by -11.
- 11 d / - 11 = - 33 / - 11
d = 3
Now let's plug d = 3 in an original equation:
4 c − 3 d = 1
4 c − 3 ∙ 3 = 1
4 c − 9 = 1
Add 9 to both sides.
4 c = 10
Divide both sides by 4
c = 10 / 4 = 2 ∙ 5 / 2 ∙ 2
c = 5 / 2
Answer:
c = 5 / 2 and d = 3
To solve the system of equations using the elimination method, follow these steps:
1. Multiply one or both of the equations by a constant to make the coefficients of one of the variables cancel each other out when added or subtracted.
Let's start by multiplying the first equation by 2 and the second equation by 4 to make the coefficients of 'c' in both equations equal:
Equation 1: 2 * (4c - 3d) = 2 * 1 becomes 8c - 6d = 2
Equation 2: 4 * (2c + 4d) = 4 * 17 becomes 8c + 16d = 68
2. Now, subtract one equation from the other to eliminate one variable.
Subtract the equation we obtained in step 1 (equation 1) from equation 2:
(8c + 16d) - (8c - 6d) = 68 - 2
Simplifying the equation:
8c + 16d - 8c + 6d = 66
22d = 66
3. Solve for the remaining variable.
Divide both sides of the equation by 22:
22d / 22 = 66 / 22
Simplifying:
d = 3
4. Substitute the value of 'd' back into one of the original equations to solve for 'c'.
Let's substitute 'd = 3' into equation 1:
4c - 3(3) = 1
Simplifying:
4c - 9 = 1
Add 9 to both sides:
4c = 10
Divide both sides by 4:
c = 10 / 4
Simplifying:
c = 2.5
Therefore, the solution to the system of equations is c = 2.5 and d = 3.