Question 159055
1.{{{y = x^2-6x+6}}}
2.{{{y-x=-4}}}
Use eq. 2 and find an expression for y in terms of x.
2.{{{y-x=-4}}}
{{{y=x-4}}}
Substitute into eq. 1 and solve for x.
1.{{{y = x^2-6x+6}}}
{{{x-4 = x^2-6x+6}}}
{{{x^2-7x+10=0}}}
{{{(x-5)(x-2)=0}}}
Two solutions, first find x, then corresponding y.
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{{{(x-5)=0}}}
{{{x=5}}}
From eq. 2,
{{{y=x-4}}}
{{{y=5-4}}}
{{{y=1}}}
First solution : x=5, y=1
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{{{(x-2)=0}}}
{{{x=2}}}
from eq. 2,
{{{y=x-4}}}
{{{y=2-4}}}
{{{y=-2}}}
Second solution : x=2, y=-2
Check the solutions graphically by plotting both curves,
{{{drawing( 300, 300, -2, 7, -5, 5,grid( 1 ),circle( 2, -2, .15 ),circle( 5, 1, .15 ),
 graph( 300, 300, -2, 7, -5, 5, x-4, x^2-6x+6) )}}}