Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
{
1
4
x
−
1
3
y
=
3
2
1
4
x
+
3
4
y
=
5
2
\left\{\begin{array}{l}\frac{1}{4} x-\frac{1}{3} y=\frac{3}{2} \\ \frac{1}{4} x+\frac{3}{4} y=\frac{5}{2}\end{array}\right.
{
4
1
x
−
3
1
y
=
2
3
4
1
x
+
4
3
y
=
2
5
View step-by-step help
Home
Math Problems
Algebra 1
Multiplication with rational exponents
Full solution
Q.
{
1
4
x
−
1
3
y
=
3
2
1
4
x
+
3
4
y
=
5
2
\left\{\begin{array}{l}\frac{1}{4} x-\frac{1}{3} y=\frac{3}{2} \\ \frac{1}{4} x+\frac{3}{4} y=\frac{5}{2}\end{array}\right.
{
4
1
x
−
3
1
y
=
2
3
4
1
x
+
4
3
y
=
2
5
Write Equations:
Step
1
1
1
: Write down the
system of equations
.
\newline
(
1
4
)
x
−
(
1
3
)
y
=
3
2
(\frac{1}{4})x - (\frac{1}{3})y = \frac{3}{2}
(
4
1
)
x
−
(
3
1
)
y
=
2
3
,
(
1
4
)
x
+
(
3
4
)
y
=
5
2
(\frac{1}{4})x + (\frac{3}{4})y = \frac{5}{2}
(
4
1
)
x
+
(
4
3
)
y
=
2
5
Clear Fractions:
Step
2
2
2
: Multiply the first equation by
12
12
12
to clear the
fractions
.
\newline
12
×
[
(
1
4
)
x
−
(
1
3
)
y
=
3
2
]
12 \times \left[\left(\frac{1}{4}\right)x - \left(\frac{1}{3}\right)y = \frac{3}{2}\right]
12
×
[
(
4
1
)
x
−
(
3
1
)
y
=
2
3
]
\newline
3
x
−
4
y
=
18
3x - 4y = 18
3
x
−
4
y
=
18
Solve for x:
Step
3
3
3
: Multiply the second equation by
4
4
4
to clear the fractions.
\newline
4
×
[
(
1
4
)
x
+
(
3
4
)
y
=
5
2
]
4 \times \left[\left(\frac{1}{4}\right)x + \left(\frac{3}{4}\right)y = \frac{5}{2}\right]
4
×
[
(
4
1
)
x
+
(
4
3
)
y
=
2
5
]
\newline
x
+
3
y
=
10
x + 3y = 10
x
+
3
y
=
10
Solve for y:
Step
4
4
4
: Solve for x from the second equation.
\newline
x
=
10
−
3
y
x = 10 - 3y
x
=
10
−
3
y
Substitute x:
Step
5
5
5
: Substitute x in the first equation.
\newline
3
(
10
−
3
y
)
−
4
y
=
18
3(10 - 3y) - 4y = 18
3
(
10
−
3
y
)
−
4
y
=
18
\newline
30
−
9
y
−
4
y
=
18
30 - 9y - 4y = 18
30
−
9
y
−
4
y
=
18
\newline
30
−
13
y
=
18
30 - 13y = 18
30
−
13
y
=
18
Solve for y:
Step
6
6
6
: Solve for y.
\newline
−
13
y
=
18
−
30
-13y = 18 - 30
−
13
y
=
18
−
30
\newline
−
13
y
=
−
12
-13y = -12
−
13
y
=
−
12
\newline
y
=
−
12
/
−
13
y = -12 / -13
y
=
−
12/
−
13
\newline
y
=
12
13
y = \frac{12}{13}
y
=
13
12
Substitute y:
Step
7
7
7
: Substitute
y
y
y
back into the equation for
x
x
x
.
x
=
10
−
3
(
12
13
)
x = 10 - 3\left(\frac{12}{13}\right)
x
=
10
−
3
(
13
12
)
x
=
10
−
36
13
x = 10 - \frac{36}{13}
x
=
10
−
13
36
x
=
130
13
−
36
13
x = \frac{130}{13} - \frac{36}{13}
x
=
13
130
−
13
36
x
=
94
13
x = \frac{94}{13}
x
=
13
94
More problems from Multiplication with rational exponents
Question
Simplify.
\newline
8
1
1
2
81^{\frac{1}{2}}
8
1
2
1
\newline
_____________
Get tutor help
Posted 1 year ago
Question
Simplify.
\newline
(
−
32
)
1
/
5
(-32)^{1/5}
(
−
32
)
1/5
\newline
______
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
w
4
3
w
7
3
\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}
w
3
7
w
3
4
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Posted 9 months ago
Question
Simplify. Assume all variables are positive.
\newline
(
2
r
1
3
)
8
(2r^{\frac{1}{3}})^8
(
2
r
3
1
)
8
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Posted 9 months ago
Question
Simplify. Assume all variables are positive.
\newline
v
7
4
⋅
v
9
4
v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}
v
4
7
⋅
v
4
9
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
\newline
Get tutor help
Posted 9 months ago
Question
Simplify.
\newline
1
1
4
⋅
1
1
4
1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}
1
4
1
⋅
1
4
1
\newline
______
Get tutor help
Posted 9 months ago
Question
Simplify.
\newline
3
2
(
−
1
/
5
)
32^{(-1/5)}
3
2
(
−
1/5
)
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
w
3
2
w
5
2
\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}
w
2
5
w
2
3
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
\newline
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
(
27
x
)
2
3
(27x)^{\frac{2}{3}}
(
27
x
)
3
2
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
x
1
4
x
11
4
\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}
x
4
11
x
4
1
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
\newline
Get tutor help
Posted 1 year ago
Related topics
Algebra - Order of Operations
Algebra - Distributive Property
`X` and `Y` Axes
Geometry - Scalene Triangle
Common Multiple
Geometry - Quadrant