y = -x + 4 and x + 2y = -8, how many solutions does this linear system have?

Solution:

Given set of equations y = -x + 4 and x + 2y = -8

Let y = -x + 4 --- [a]

Let x + 2y = -8 --- [b]

Rearrange eq[a] as x + y = 4

Let us use the elimination method to solve the system of linear equation.

Subtract eq[b] from eq[a]

x + y = 4
x + 2y = -8
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-y = 12

y = -12

Put y = -12 in eq[a] we get,

⇒ x + (-12) = 4

⇒ x - 12 = 4

⇒ x = 4 + 12 = 16

⇒ x = 16

Therefore, the set of equations has only one set of solution (16, -12)

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y = -x + 4 and x + 2y = -8, how many solutions does this linear system have?

Summary:

The linear set of equations y = -x + 4 and x + 2y = -8, have only 1 solution.