Asked by AYD3N

x 2x -2y = 6
3x + 2y = 9
Solve the system of equations.


Ax A x=0, y =3


x B x=3, y= 0


•x C x=1,y=-2


1x D x=-2, y= 1
-×

x= 6, y = 3
Answered by AYD3N
4x 5x + 5y = 140
3x + 9y = 162
What is the solution for the system of equations above?

A
✕ =12,y=16
《×

B x = 16, y = 12
《×
C
x =13, y = 15
《×

x=15, y = 13
Answered by AYD3N
× 6x + 3y = 9
2x + 3y = 1
Solve the system of equations.
4x
A
x=2, y=-1
x B x=-1, y =2
C
1
X= -1/2, y=3
D
x = 3, y=_1
1x E x=1, y= 1
Answered by AYD3N
1× 4x+7y=-33
7x-3y =49
What is the solution for the system of equations above?
_x
A
x = 4, y = -7

B
X=-4，ソニー7
X
C
X=3,y=-7

D
x= -3, y = 7
Answered by AYD3N
1× 9х + 3y=-27
3x + 14y=-48
What is the solution for the system of equations above?
A x=4, y=-3
X=-2,y=-4
x=2, y= 3
xD
X=-2，ノ=-3
Answered by AYD3N
1× 3x-y=4
x + 2y = 6
Solve the system of equations.
(-2,-2)
(2,-2)
(2.5,1.75)
』x
(2.5,4.75)
(2,2)
Answered by GPT-4o mini
To solve the system of equations:

1. \( 2x - 2y = 6 \)
2. \( 3x + 2y = 9 \)

Let's solve it step by step.

**Step 1:** Simplify the first equation.

Divide the first equation by 2:

\[
x - y = 3 \quad \text{(Equation 1)}
\]

**Step 2:** Rearrange Equation 1 to express \(y\) in terms of \(x\):

\[
y = x - 3 \quad \text{(Equation 2)}
\]

**Step 3:** Substitute Equation 2 into the second equation:

Substituting for \(y\) in Equation 2:

\[
3x + 2(x - 3) = 9
\]

Simplifying this gives:

\[
3x + 2x - 6 = 9
\]

Combine like terms:

\[
5x - 6 = 9
\]

Add 6 to both sides:

\[
5x = 15
\]

Divide by 5:

\[
x = 3 \quad \text{(Value of x)}
\]

**Step 4:** Now substitute \(x = 3\) back into Equation 2 to find \(y\):

\[
y = 3 - 3 = 0 \quad \text{(Value of y)}
\]

**Final Solution:** The solution to the system of equations is \(x = 3\) and \(y = 0\).

Thus, the answer is:

**B**: \(x = 3, y = 0\).
Answered by GPT-4o mini
To solve the system of equations:

1. \( 5x + 5y = 140 \)
2. \( 3x + 9y = 162 \)

Let's solve it step by step.

**Step 1:** Simplify the first equation.

Divide the entire first equation by 5:

\[
x + y = 28 \quad \text{(Equation 1)}
\]

**Step 2:** Rearrange Equation 1 to express \(y\) in terms of \(x\):

\[
y = 28 - x \quad \text{(Equation 2)}
\]

**Step 3:** Substitute Equation 2 into the second equation:

Now, substitute for \(y\) in the second equation:

\[
3x + 9(28 - x) = 162
\]

Distributing \(9\):

\[
3x + 252 - 9x = 162
\]

Combine like terms:

\[
-6x + 252 = 162
\]

Subtract 252 from both sides:

\[
-6x = 162 - 252
\]

\[
-6x = -90
\]

Divide by -6:

\[
x = 15 \quad \text{(Value of x)}
\]

**Step 4:** Now substitute \(x = 15\) back into Equation 2 to find \(y\):

\[
y = 28 - 15 = 13 \quad \text{(Value of y)}
\]

**Final Solution:** The solution to the system of equations is \(x = 15\) and \(y = 13\).

Thus, the answer is:

**D**: \(x = 15, y = 13\).
Answered by GPT-4o mini
To solve the system of equations:

1. \( 6x + 3y = 9 \)
2. \( 2x + 3y = 1 \)

Let's solve it step by step.

**Step 1:** Simplify the first equation.

Divide the entire first equation by 3:

\[
2x + y = 3 \quad \text{(Equation 1)}
\]

The second equation remains as is:

\[
2x + 3y = 1 \quad \text{(Equation 2)}
\]

**Step 2:** Now we have the system:

1. \( 2x + y = 3 \) (Equation 1)
2. \( 2x + 3y = 1 \) (Equation 2)

**Step 3:** Subtract Equation 1 from Equation 2 to eliminate \(2x\):

\[
(2x + 3y) - (2x + y) = 1 - 3
\]

This simplifies to:

\[
2y = -2
\]

Dividing both sides by 2 gives:

\[
y = -1
\]

**Step 4:** Substitute \(y = -1\) back into Equation 1 to find \(x\):

\[
2x + (-1) = 3
\]

This simplifies to:

\[
2x - 1 = 3
\]

Adding 1 to both sides gives:

\[
2x = 4
\]

Dividing by 2 gives:

\[
x = 2
\]

**Final Solution:** The solution to the system of equations is \(x = 2\) and \(y = -1\).

Thus, the answer is:

**A**: \(x = 2, y = -1\).
Answered by GPT-4o mini
To solve the system of equations:

1. \( 4x + 7y = -33 \)
2. \( 7x - 3y = 49 \)

Let's solve it step by step.

**Step 1:** We'll use the elimination method. First, we can eliminate one variable by manipulating the equations. Let's solve for \(y\) from the first equation.

From the first equation:

\[
7y = -33 - 4x \quad \text{(Equation 1)}
\]
This gives:

\[
y = \frac{-33 - 4x}{7} \quad \text{(Equation 2)}
\]

**Step 2:** Substitute Equation 2 for \(y\) in the second equation:

\[
7x - 3\left(\frac{-33 - 4x}{7}\right) = 49
\]

Multiply through by 7 to eliminate the fraction:

\[
49x + 3(33 + 4x) = 343
\]

This simplifies to:

\[
49x + 99 + 12x = 343
\]

Combine like terms:

\[
61x + 99 = 343
\]

**Step 3:** Subtract 99 from both sides:

\[
61x = 244
\]

Now, divide by 61:

\[
x = \frac{244}{61} = 4
\]

**Step 4:** Substitute \(x = 4\) back into Equation 1 to find \(y\):

\[
4(4) + 7y = -33
\]
\[
16 + 7y = -33
\]
\[
7y = -33 - 16
\]
\[
7y = -49
\]

Now divide by 7:

\[
y = -7
\]

**Final Solution:** The solution to the system of equations is \(x = 4\) and \(y = -7\).

Thus, the answer is:

**A**: \(x = 4, y = -7\).
Answered by GPT-4o mini
To solve the system of equations:

1. \( 9x + 3y = -27 \)
2. \( 3x + 14y = -48 \)

Let's solve it step by step.

**Step 1:** Simplify the first equation.

We can divide the entire first equation by 3:

\[
3x + y = -9 \quad \text{(Equation 1)}
\]

The second equation remains unchanged:

\[
3x + 14y = -48 \quad \text{(Equation 2)}
\]

**Step 2:** Now we have the system:

1. \( 3x + y = -9 \)
2. \( 3x + 14y = -48 \)

**Step 3:** We can subtract Equation 1 from Equation 2:

\[
(3x + 14y) - (3x + y) = -48 - (-9)
\]

This simplifies to:

\[
14y - y = -48 + 9
\]

Combine like terms:

\[
13y = -39
\]

Dividing by 13:

\[
y = -3 \quad \text{(Value of y)}
\]

**Step 4:** Substitute \(y = -3\) back into Equation 1 to find \(x\):

\[
3x + (-3) = -9
\]

This simplifies to:

\[
3x - 3 = -9
\]

Adding 3 to both sides yields:

\[
3x = -6
\]

Dividing by 3 gives:

\[
x = -2 \quad \text{(Value of x)}
\]

**Final Solution:** The solution to the system of equations is \(x = -2\) and \(y = -3\).

Thus, the answer is:

**D**: \(x = -2, y = -3\).
Answered by GPT-4o mini
To solve the system of equations:

1. \( 3x - y = 4 \)
2. \( x + 2y = 6 \)

Let's solve it step by step.

**Step 1:** We can rearrange the first equation to express \(y\) in terms of \(x\):

From the first equation:

\[
y = 3x - 4 \quad \text{(Equation 1)}
\]

**Step 2:** Now substitute Equation 1 into the second equation:

Using \(y = 3x - 4\) in the second equation \(x + 2y = 6\):

\[
x + 2(3x - 4) = 6
\]

**Step 3:** Distribute the \(2\):

\[
x + 6x - 8 = 6
\]

Combine like terms:

\[
7x - 8 = 6
\]

**Step 4:** Add \(8\) to both sides:

\[
7x = 14
\]

**Step 5:** Divide by \(7\):

\[
x = 2
\]

**Step 6:** Substitute \(x = 2\) back into Equation 1 to find \(y\):

\[
y = 3(2) - 4 = 6 - 4 = 2
\]

**Final Solution:** The solution to the system of equations is \(x = 2\) and \(y = 2\).

Thus, the answer is:

**(2, 2)**.