What is the value of y? 5x–2y=4 and 10x–4y=8.
Answers
Step-by-step explanation:
Solve by Substitution 5x+2y=4 , 10x+4y=8
5
x
+
2
y
=
4
,
10
x
+
4
y
=
8
Solve for
x
in the first equation.
Subtract
2
y
from both sides of the equation.
5
x
=
4
−
2
y
10
x
+
4
y
=
8
Divide each term by
5
and simplify.
Divide each term in
5
x
=
4
−
2
y
by
5
.
5
x
5
=
4
5
+
−
2
y
5
10
x
+
4
y
=
8
Cancel the common factor of
5
.
Cancel the common factor.
5
x
5
=
4
5
+
−
2
y
5
10
x
+
4
y
=
8
Divide
x
by
1
.
x
=
4
5
+
−
2
y
5
10
x
+
4
y
=
8
Move the negative in front of the fraction.
x
=
4
5
−
2
y
5
10
x
+
4
y
=
8
Replace all occurrences of
x
in
10
x
+
4
y
=
8
with
4
5
−
2
y
5
.
x
=
4
5
−
2
y
5
10
(
4
5
−
2
y
5
)
+
4
y
=
8
Simplify
10
(
4
5
−
2
y
5
)
+
4
y
Simplify each term.
Apply the distributive property.
x
=
4
5
−
2
y
5
10
(
4
5
)
+
10
(
−
2
y
5
)
+
4
y
=
8
Cancel the common factor of
5
Factor
5
out of
10
.
x
=
4
5
−
2
y
5
5
(
2
)
(
4
5
)
+
10
(
−
2
y
5
)
+
4
y
=
8
Cancel the common factor.
x
=
4
5
−
2
y
5
5
⋅
(
2
(
4
5
)
)
+
10
(
−
2
y
5
)
+
4
y
=
8
Rewrite the expression.
x
=
4
5
−
2
y
5
2
⋅
4
+
10
(
−
2
y
5
)
+
4
y
=
8
Multiply
2
by
4
.
x
=
4
5
−
2
y
5
8
+
10
(
−
2
y
5
)
+
4
y
=
8
Cancel the common factor of
5
Move the leading negative in
−
2
y
5
into the numerator.
x
=
4
5
−
2
y
5
8
+
10
(
−
2
y
5
)
+
4
y
=
8
Factor
5
out of
10
.
x
=
4
5
−
2
y
5
8
+
5
(
2
)
(
−
2
y
5
)
+
4
y
=
8
Cancel the common factor.
x
=
4
5
−
2
y
5
8
+
5
⋅
(
2
(
−
2
y
5
)
)
+
4
y
=
8
Rewrite the expression.
x
=
4
5
−
2
y
5
8
+
2
(
−
2
y
)
+
4
y
=
8
Multiply
−
2
by
2
.
x
=
4
5
−
2
y
5
8
−
4
y
+
4
y
=
8
Combine the opposite terms in
8
−
4
y
+
4
y
...
Add
−
4
y
and
4
y
.
x
=
4
5
−
2
y
5
8
+
0
=
8
Add
8
and
0
.
x
=
4
5
−
2
y
5
8
=
8
Since
8
=
8
, the equation will always be true.
x
=
4
5
−
2
y
5
Always true
Remove any equations from the system that are always true.
x
=
4
5
−
2
y
5
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