Complete the following activity to solve the simultaneons equations 3x-2y=3 and 2x+y=16 by cramer's rule
Answers
Answer:
Writing the system of equations in matrix form AX=B
where A is the 2×2 coefficient matrix, X=(
x
y
) and B is the 2×1 matrix of constants.
Here, A=(
3
2
−2
1
) and B=(
3
16
)
We can write, X=A
−1
B, where
A
−1
=
∣A∣
1
adj(A)
A
−1
=
7
1
×(
1
−2
2
3
)
Substituting the values we get,
(
x
y
)=
7
1
×(
1
−2
2
3
) ×(
3
16
)
(
x
y
)=
7
1
×(
3×1+2×16
(−2)×3+3×16
)
(
x
y
)= (
5
6
).
Hence, x=5 and y=6.
Step-by-step explanation:
Writing the system of equations in matrix form AX=B
where A is the 2×2 coefficient matrix, X=(
x
y
) and B is the 2×1 matrix of constants.
Here, A=(
3
2
−2
1
) and B=(
3
16
)
We can write, X=A
−1
B, where
A
−1
=
∣A∣
1
adj(A)
A
−1
=
7
1
×(
1
−2
2
3
)
Substituting the values we get,
(
x
y
)=
7
1
×(
1
−2
2
3
) ×(
3
16
)
(
x
y
)=
7
1
×(
3×1+2×16
(−2)×3+3×16
)
(
x
y
)= (
5
6
).
Hence, x=5 and y=6.