SOLUTION: Solve the system of equations. 1. y = x - 1 x^2 + y^2 = 25 2. x + y = 1 y = x^2 - 5

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the system of equations. 1. y = x - 1 x^2 + y^2 = 25 2. x + y = 1 y = x^2 - 5       Log On


   

Question 1059193: Solve the system of equations.
1.
y = x - 1
x^2 + y^2 = 25
2.
x + y = 1
y = x^2 - 5
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

1. Substitute "x-1" for "y" in the 2nd equation, to get:
+x%5E2+%2B+%28x-1%29%5E2+=+25+
+x%5E2+%2B+%28x%5E2+-+2x+%2B+1%29+=+25+
++2x%5E2+-+2x+%2B+1+=+25+
++2x%5E2+-+2x+-+24+=+0+
+++x%5E2+-+x+-+12+=+0+
++%28x%2B3%29%28x-4%29+=+0+
So x=-3 or x=4
x=-3 ==> y=-4
x=4 ==> y=3
—
Answer: (x,y) = (-3, -4) and (x,y) = (4,3)
—
Check:
+%28-3%29%5E2+%2B+%28-4%29%5E2+=+9+%2B+16+=+25+ (ok)
and
+%284%29%5E2+%2B+%283%29%5E2+=+16+%2B+9+=+25+ (ok)
——
2. x+y = 1 ==> y=1-x
Substitute 1-x for y in the 2nd equation to get:
+1-x+=+x%5E2+-+5+
+x%5E2+%2B+x+-+6+=+0+
+%28x-2%29%28x%2B3%29+=+0+
x=2 or x=-3
x=2 ==> y=-1
x=-3 ==> y=4
—
Answer: (x,y) = (2,-1) and (x,y) = (-3,4)
—
Check:
+2%5E2+-5+=+4-5+=+-1+ (ok)
+%28-3%29%5E2+-+5+=+9-5+=+4++ (ok)