Solving Syslems of Equolions
SOI,VE THE SYSTEM OF EQUATIONS
x*Y=5
-2x.tY=4
l)
BY GRAPH|NG
ln eoch equolion, find the x ond y infercepfs.
x*y=5
x *0=5
x=5
x*y=5
O+y-5
y=5
Plot lhe
x
-2xty=4 Iety-O
lety=g
xintercept
-2x*Q='4
ond y infercepfs
f
x
intercept
'2x*Y=4 letx=0
O+ y--4
lefx=0
yintercept
x:-A z
(5rO)
(Or5)
y ='4
y
intercept
(O,-4)
or both eguofions.
Ihe solufion occurs where the lines inlersecf on fhe groph.
Resufi:x=3
Thank you to the Academic Learning Centers at Union County College
www.ucc.edu
y=2
(2,O)
Solving Syslems of Equqtions
2l BY EUMINATTON
x*Y=5
-2x*Y=4
Multiply both srdes of the first eguofio n by 2.
2(x+y) =(5)2
2xr- 2y - l0
Add the lwo equolions fogefher to eliminote x.
2x* 2Y = l0
*-2x-l y- -4
lnserl
3Y=6
Y=2
2 inlo either eguofion for y lo solve for x.
x* y- 5
y* 2= 5
Result:x=3 y=2
x =3
3)
BY SUBSTTTUTTON
x*Y=5
-2x* y =4
inoneequotion.
Solvefor y
Subsfifufe lhe resuh (2x
-
y
=2x-4
4) for y in the other equofion.
x * y
=5
3x-4=5
x * (2x-41=5
3x=9
x=3
lnserl 3 info one eguolion for
x
ond solve for y.
x* y- 5
3* y=5
Result: x=3 y=2
Y=2
Thank you to the Academic Learning Centers at Union County College
www.ucc.edu