Question

How do you solve the system of equations: `x+ 2y = 8; - y = - 2x + 6`?

Answer 1

The lines from each equation intersect at point `P` such that:

`P->(x,y)=(4,2)`

Explanation:

Given:
`-y=-2x+6.....................Equation(1)`
`x+2y=8............................Equation(2)`
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`color(blue)("Determine the value of "x)`

Consider equation(1)
Multiply both sides by (-1) giving

`+y=+2x-6........................Eqiation(1_a)`

Substitute for `y` in `Equation(2)` using `Equation(1_a)`

`x+2y=8" "->" "x+2(2x-6)=8`

`x+4x-12=8`

`5x-12=8`

Add 12 to both sides

`5x=20`

Divide both sides by 5

`color(blue)(x=4)`
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`color(blue)("Determine the value of "y)`

Substitute for `x` in `Equation(1)`

`-y=-2x+6" "->" "-y=-2(4)+6`

Multiply both sides by (-1)

`y=8-6`

`color(blue)(y=2)`