Question

Đã trả lời bởi chuyên gia

Answer 1

To solve the system of equations:

1. \( x - 2y = 3 \)
2. \( 3x - 4y = 2 \)

We can use the method of substitution or elimination. Let's use the substitution method here:

From equation (1), solve for \( x \):

\[ x = 3 + 2y \]

Now substitute \( x \) in equation (2):

\[ 3(3 + 2y) - 4y = 2 \]

Expand and simplify:

\[ 9 + 6y - 4y = 2 \]
\[ 2y + 9 = 2 \]

Subtract 9 from both sides:

\[ 2y = 2 - 9 \]
\[ 2y = -7 \]

Divide both sides by 2 to solve for \( y \):

\[ y = -\frac{7}{2} \]

Now substitute \( y = -\frac{7}{2} \) back into \( x = 3 + 2y \):

\[ x = 3 + 2(-\frac{7}{2}) \]
\[ x = 3 - 7 \]
\[ x = -4 \]

Therefore, the solution to the system of equations is \( x = -4 \) and \( y = -\frac{7}{2} \).

To verify:
Substitute \( x = -4 \) and \( y = -\frac{7}{2} \) back into the original equations:

For equation (1):
\[ -4 - 2(-\frac{7}{2}) = 3 \]
\[ -4 + 7 = 3 \]
\[ 3 = 3 \] (True)

For equation (2):
\[ 3(-4) - 4(-\frac{7}{2}) = 2 \]
\[ -12 + 14 = 2 \]
\[ 2 = 2 \] (True)

Therefore, the solution \( x = -4 \) and \( y = -\frac{7}{2} \) satisfies both equations, confirming our solution is correct.

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Answer 2

To solve the system of equations:

1. \( x - 2y = 3 \)
2. \( 3x - 4y = 2 \)

We can use the method of substitution or elimination. Let's use the substitution method here:

From equation (1), solve for \( x \):

\[ x = 3 + 2y \]

Now substitute \( x \) in equation (2):

\[ 3(3 + 2y) - 4y = 2 \]

Expand and simplify:

\[ 9 + 6y - 4y = 2 \]
\[ 2y + 9 = 2 \]

Subtract 9 from both sides:

\[ 2y = 2 - 9 \]
\[ 2y = -7 \]

Divide both sides by 2 to solve for \( y \):

\[ y = -\frac{7}{2} \]

Now substitute \( y = -\frac{7}{2} \) back into \( x = 3 + 2y \):

\[ x = 3 + 2(-\frac{7}{2}) \]
\[ x = 3 - 7 \]
\[ x = -4 \]

Therefore, the solution to the system of equations is \( x = -4 \) and \( y = -\frac{7}{2} \).

To verify:
Substitute \( x = -4 \) and \( y = -\frac{7}{2} \) back into the original equations:

For equation (1):
\[ -4 - 2(-\frac{7}{2}) = 3 \]
\[ -4 + 7 = 3 \]
\[ 3 = 3 \] (True)

For equation (2):
\[ 3(-4) - 4(-\frac{7}{2}) = 2 \]
\[ -12 + 14 = 2 \]
\[ 2 = 2 \] (True)

Therefore, the solution \( x = -4 \) and \( y = -\frac{7}{2} \) satisfies both equations, confirming our solution is correct.

Answer 3

x−2y=3
Trừ x khỏi cả hai vế.

−2y=3−x
Chia cả hai vế cho −2.

−2−2y=−23−x
Việc chia cho −2 sẽ làm mất phép nhân với −2.

y=−23−x
Chia 3−x cho −2.

y=2x−3

Answer 4

x-2y=3(1)

3x-4y=2(2)

nhân (1) với 2 ta có :

2x-4y=6(3)

trừ (2) với (3):

x=-4

\Rightarrow

y=

\frac{- 7}{2}

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