What is the solution to the system of equations? y = 1/3x - 10 and 2x + y = 4

Solution:

It is given that

y = 1/3x - 10 … (1)

2x + y = 4 … (2)

Let us use the substitution method to solve the system of linear equations.

Substituting (1) in (2)

2x + (1/3 x - 10) = 4

By further calculation

2x + 1/3 x - 10 = 4

2x + 1/3 x = 4 + 10

Taking LCM

(6 + 1)/3 x = 14

7/3 x = 14

By cross multiplication

7x = 14 × 3

7x = 42

Divide both sides by 7

x = 6

Substitute the value of x in equation (1)

y = 1/3 (6) - 10

So we get

y = 2 - 10

y = -8

Therefore, the solution to the system of equations is (6, -8).

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What is the solution to the system of equations? y = 1/3x - 10 and 2x + y = 4

Summary:

The solution to the system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).