y = -6x + 2 and -12x - 2y = -4, how many solutions does this linear system have?

Solution:

Given, equations are

y= -6x + 2 --- (1)

-12x - 2y = -4 --- (2)

Substituting the value of y in (2)

-12x - 2(-6x + 2) = -4

-12x + 12x - 4 = -4

- 4 = -4

Therefore, there will be infinitely many solutions.

Example:

How many solutions does this linear system have? y = x + 2 and 6x - 4y = -10

Solution:

Given, y = x + 2 --- (1)

6x - 4y = -10 --- (2)

Substituting (1) in (2)

6x - 4(x + 2) = -10

6x - 4x - 8 = -10

Grouping of common terms,

6x - 4x = -10 + 8

2x = -2

x = -1

Put the value of x = -1 in (1)

y = -1 + 2

y = 1

Therefore, the solution is x = -1 and y = 1.

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y = -6x + 2 and -12x - 2y = -4, how many solutions does this linear system have?

Summary:

The linear system of equations y = -6x + 2 and -12x - 2y = -4 has infinitely many solutions.