if 28x + 22y =50 and 22x+28y=150 then x+y = ____
Answers
Step-by-step explanation:
Let's solve your system by substitution.
28x+22y=50 and 22x+28y=150x+y
Rewrite equations:
28x+22y=50;22x+28y=150x+y
Step: Solve28x+22y=50for x:
28x+22y=50
28x+22y+−22y=50+−22y(Add -22y to both sides)
28x=−22y+50
28x
28
=
−22y+50
28
(Divide both sides by 28)
x=
−11
14
y+
25
14
Step: Substitute
−11
14
y+
25
14
forxin22x+28y=150x+y:
22x+28y=150x+y
22(
−11
14
y+
25
14
)+28y=150(
−11
14
y+
25
14
)+y
75
7
y+
275
7
=
−818
7
y+
1875
7
(Simplify both sides of the equation)
75
7
y+
275
7
+
818
7
y=
−818
7
y+
1875
7
+
818
7
y(Add 818/7y to both sides)
893
7
y+
275
7
=
1875
7
893
7
y+
275
7
+
−275
7
=
1875
7
+
−275
7
(Add (-275)/7 to both sides)
893
7
y=
1600
7
893
7
y
893
7
=
1600
7
893
7
(Divide both sides by 893/7)
y=
1600
893
Step: Substitute
1600
893
foryinx=
−11
14
y+
25
14
:
x=
−11
14
y+
25
14
x=
−11
14
(
1600
893
)+
25
14
x=
675
1786
(Simplify both sides of the equation)
Answer:
x=675/1786 and
y=1600/893