SOLUTION: Please help me solve these systems of equations using any algebra: {{{x^2 + y = 8 }}} {{{ x-2y=-6}}} Thanks in advance!

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Please help me solve these systems of equations using any algebra: {{{x^2 + y = 8 }}} {{{ x-2y=-6}}} Thanks in advance!      Log On


   

Question 456723: Please help me solve these systems of equations using any algebra:
x%5E2+%2B+y+=+8+
+x-2y=-6
Thanks in advance!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+y+=+8+.....1
+x-2y=-6.........2...solve for x

+x=2y-6.........2...substitute in 1 and solve for y
%282y-6%29%5E2+%2B+y+=+8+.....1
4y%5E2-24y%2B36+%2B+y+=+8+
4y%5E2-23y%2B36-+8=0+
4y%5E2-23y%2B28=0+.....use quadratic formula

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

y+=+%28-%28-23%29+%2B-+sqrt%28%28-23%29%5E2-4%2A4%2A28+%29%29%2F%282%2A4%29+

y+=+%2823+%2B-+sqrt%28529-448+%29%29%2F8+

y+=+%2823+%2B-+sqrt%2881+%29%29%2F8+

y+=+%2823+%2B-+9%29%2F8+
solutions:
y+=+%2823+%2B9%29%2F8+
y+=+32%2F8+
y+=+4+
or
y+=+%2823+-9%29%2F8+
y+=+14%2F8+
y+=+1.75
now find x:

+x=2y-6
+x=2%2A4-6
+x=8-6
+x=2
or
+x=2%2A1.75-6
+x=-2.5
finally:
one solution is +x=2 and +y=4
another solution is +x=-2.5 and +y=1.75
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2+%2B8%2C%281%2F2%29x%2B3%29+