Solve:- 5ax+6by=28 , 3ax+4by=18 using cross multiplication method
X=36-28/5a y=6/b
To solve the given set of equations using the cross multiplication method, follow these steps:
Step 1: Rearrange the equations in the form of "ax + by = c".
Equations given: 5ax + 6by = 28, and 3ax + 4by = 18.
Rearranging the first equation:
5ax + 6by = 28
5ax = 28 - 6by
ax = (28 - 6by) / 5
Now, rearranging the second equation:
3ax + 4by = 18
3ax = 18 - 4by
ax = (18 - 4by) / 3
Step 2: Equate the two expressions of "ax" obtained in the above rearrangements since they are both equal to "ax".
(28 - 6by) / 5 = (18 - 4by) / 3
Step 3: Cross multiply by multiplying the numerator of the left-hand side (LHS) with the denominator of the right-hand side (RHS) and vice versa.
3(28 - 6by) = 5(18 - 4by)
Step 4: Simplify the equation obtained by expanding and combining like terms.
(84 - 18by) = (90 - 20by)
Step 5: Eliminate the parentheses by distributing the numbers.
84 - 18by = 90 - 20by
Step 6: Rearrange the equation to isolate terms with "by" on one side and constants on the other.
-18by + 20by = 90 - 84
2by = 6
Step 7: Simplify the equation by combining like terms.
2by = 6
Step 8: Solve for "by" by dividing both sides of the equation by 2.
by = 6 / 2
by = 3
Step 9: Substitute the value of "by" back into one of the original equations to find the value of "ax".
Using the first equation, we have:
5ax + 6(3) = 28
5ax + 18 = 28
5ax = 28 - 18
5ax = 10
Now, divide both sides of the equation by 5 to solve for "ax".
ax = 10 / 5
ax = 2
Step 10: Verify the solution by substituting the values of "ax" and "by" into the second equation.
Using the second equation:
3(2) + 4(3) = 18
6 + 12 = 18
18 = 18
Therefore, the solution to the given set of equations is:
ax = 2
by = 3