7x+2y =5
3 X + 4 y =8
Answers
Step-by-step explanation:
Explanation:
you are given a 2 equation and you need to find both x and y
{
7
x
−
2
y
=
8
3
x
−
4
y
=
7
there are two solutions and they have both the same answer. you will just choose what is easier.
By substitution
first let's find the value of x in first equation
7
x
−
2
y
=
8
7
x
=
8
+
2
y
→
transpose
2
y
to other side of equation to leave
7
x
x
=
8
+
2
y
7
→
divide both side by
7
then we have the x value
substitute your answer (the value of
x
) to next equation
3
⋅
(
8
+
2
y
7
)
−
4
y
=
7
24
+
6
y
7
−
4
y
=
7
24
+
6
y
7
−
4
y
=
7
∣
⋅
(
7
)
24
+
6
y
−
28
y
=
49
−
22
y
=
49
−
24
−
22
y
=
25
y
=
−
25
22
To find the value of
x
just substitute the first equation by the value of
y
.
BY ELIMINATION
{
7
x
−
2
y
=
8
3
x
−
4
y
=
7
Think of how to eliminate any one of the variables.
i think that if we multiply the first equation by
−
2
,
y
will be cancelled.
{
(
7
x
−
2
y
=
8
)
∣
⋅
(
−
2
)
3
x
−
4
y
=
7
−
14
x
+
4
y
=
−
16
3
x
−
4
y
=
7
Add the two equations to get
−
14
x
+
4
y
+
3
x
−
4
y
=
−
16
+
7
−
11
x
=
−
9
→
divide both sides by
−
11
x
=
9
11
To know the value of
y
, substitute the value of
x
in one of the equation.
3
x
−
4
y
=
7
3
⋅
(
9
11
)
−
4
y
=
7
27
11
−
4
y
=
7
−
4
y
=
7
−
27
11
−
4
y
=
50
11
→
divide both sides by
−
4
y
=
−
25
22
Answer link
Related topic
Systems Using Substitution
Questions
Related questions
How do you solve systems of equations using the substitution method?
How do you check your solutions to a systems of equations using the substitution method?
When is the substitution method easier to use?
How do you know if a solution is "no solution" or "infinite" when using the substitution method?
How do you solve
y
=
−
6
x
−
3
and
y
=
3
using the substitution method?
How do you solve
12
y
−
3
x
=
−
1
and
x
−
4
y
=
1
using the substitution method?
Which method do you use to solve the system of equations
y
=
1
4
x
−
14
and
y
=
19
8
x
+
7
?
Answer:
SUBSTITUSION METHOD:-
1 ) 7x = 5 - 2y
1 ) 7x = 5 - 2y x = 5 - 2y
1 ) 7x = 5 - 2y x = 5 - 2y 7
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 )
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22 x = -14
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22 x = -14 11
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22 x = -14 11ANS - x = -14
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22 x = -14 11ANS - x = -14 11
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22 x = -14 11ANS - x = -14 11 y = -7
1 ) 7x = 5 - 2y x = 5 - 2y 7 3 ( 5 - 2y ) + 4y = 8 7 15 - 6y + 28y = 8 22y = -7 y = -7 22 x = 5 - 2 ( -7 ) 22 x = -28 22 x = -14 11ANS - x = -14 11 y = -7 22