What is the solution to the system of linear equations? 6x + 7y = 59, 4x + 5y = 41

Solution:

Given linear equations

6x + 7y = 59 --- (a)

4x + 5y = 41 --- (b)

Let us solve them by the elimination method.

Multiply eq(a) with '4'

24x + 28y = 236 --- (a')

Multiply eq(b) with '6'

24x + 30y = 246 --- (b')

Subtract eq(b') from eq(a'), we get

⇒ -2y = -10

⇒ y = 5

Put y=5 in eq(a)

⇒ 6x + 7(5) = 59

⇒ 6x + 35 = 59

⇒ 6x = 59-35

⇒ 6x = 24

⇒ x = 24/6

⇒ x = 4

Therefore, the solution set is (4, 5)

Hence, the set of equations are consistent.

---

What is the solution to the system of linear equations? 6x + 7y = 59, 4x + 5y = 41

Summary:

The solution to the system of linear equations? 6x + 7y = 59, 4x + 5y = 41 is (4, 5).