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How do you solve y= -2x + 2 and 6x + 2y = 3?

1 Answer

Jun 18, 2018

$(x, y) = (- \frac{1}{2}, 3)$ $(x,y)=(-1/2,3)$

Explanation:

Given
[1] $XXX y = - 2 x + 2$ $color(white)("XXX")y=-2x+2$
[2] $XXX 6 x + 2 y = 3$ $color(white)("XXX")6x+2y=3$

The form given for equation [1] makes solution by substitution the most obvious method:

Base on [1] we can substitute $(- 2 x + 2)$ $(-2x+2)$ for $y$ $y$ in [2]
[3] $XXX 6 x + 2 (- 2 x + 2) = 3$ $color(white)("XXX")6x+2(-2x+2)=3$

Simplifying [3]
[4] $XXX 2 x + 4 = 3$ $color(white)("XXX")2x+4=3$
or
[5] $XXX x = - \frac{1}{2}$ $color(white)("XXX")x=-1/2$

We can now substitute $(- \frac{1}{2})$ $(-1/2)$ for $x$ $x$ in [1]
[6] $XXX y = - 2 (- \frac{1}{2}) + 2 = 3$ $color(white)("XXX")y=-2(-1/2)+2=3$

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