Question
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
3, x, minus, 4, y, equals, 0
3x−4y=
0
minus, 3, x, plus, 9, y, equals, 30
−3x+9y=
30
Answer
Multiple Choice Answers
A, d, d, to eliminate , x, .Add to eliminate x.
S, u, b, t, r, a, c, t, to eliminate , x, .Subtract to eliminate x.
S, u, b, t, r, a, c, t, to eliminate , y, .Subtract to eliminate y.
A, d, d, to eliminate , y, .Add to eliminate y
3, x, minus, 4, y, equals, 0
3x−4y=
0
minus, 3, x, plus, 9, y, equals, 30
−3x+9y=
30
Answer
Multiple Choice Answers
A, d, d, to eliminate , x, .Add to eliminate x.
S, u, b, t, r, a, c, t, to eliminate , x, .Subtract to eliminate x.
S, u, b, t, r, a, c, t, to eliminate , y, .Subtract to eliminate y.
A, d, d, to eliminate , y, .Add to eliminate y
Answers
Answer
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
minus, 8, x, minus, y, equals, 35
−8x−y=
35
minus, 8, x, minus, 5, y, equals, 15
−8x−5y=
15
Answer
Multiple Choice Answers
A, d, d, to eliminate , x, .Add to eliminate x.
A, d, d, to eliminate , y, .Add to eliminate y.
S, u, b, t, r, a, c, t, to eliminate , y, .Subtract to eliminate y.
S, u, b, t, r, a, c, t, to eliminate , x, .Subtract to eliminate x.
minus, 8, x, minus, y, equals, 35
−8x−y=
35
minus, 8, x, minus, 5, y, equals, 15
−8x−5y=
15
Answer
Multiple Choice Answers
A, d, d, to eliminate , x, .Add to eliminate x.
A, d, d, to eliminate , y, .Add to eliminate y.
S, u, b, t, r, a, c, t, to eliminate , y, .Subtract to eliminate y.
S, u, b, t, r, a, c, t, to eliminate , x, .Subtract to eliminate x.
Answer
Solve the system of equations minus, 2, x, minus, 7, y, equals, minus, 14−2x−7y=−14 and minus, x, minus, 5, y, equals, minus, 13−x−5y=−13 by combining the equations.
Below, two sets of the two equations are shown. The first set has input boxes in front of each equation to put a number to multiply it by. When you enter a number, the corresponding equation below changes to be the result of the multiplication. Under the second set, a resulting equation is shown with input boxes for the coefficients and constant. Then, there is a "try" button. When you press the try button, if your answer is correct, it will be placed on the page and a new question will appear with a new input box. This process will continue until the final answer area appears with the submit button.
left parenthesis, minus, 2, x(−2x minus, 7, y−7y equals= minus, 14, right parenthesis−14)
left parenthesis, minus, x(−x minus, 5, y−5y equals= minus, 13, right parenthesis−13)
minus, 2, x−2x minus, 7, y−7y equals= minus, 14−14
minus, x−x minus, 5, y−5y equals= minus, 13−13
0
0xx plus+
0
0yy equals=
Answer
Attempt 1 out of 2
You must answer all questions above in order to submit.
Below, two sets of the two equations are shown. The first set has input boxes in front of each equation to put a number to multiply it by. When you enter a number, the corresponding equation below changes to be the result of the multiplication. Under the second set, a resulting equation is shown with input boxes for the coefficients and constant. Then, there is a "try" button. When you press the try button, if your answer is correct, it will be placed on the page and a new question will appear with a new input box. This process will continue until the final answer area appears with the submit button.
left parenthesis, minus, 2, x(−2x minus, 7, y−7y equals= minus, 14, right parenthesis−14)
left parenthesis, minus, x(−x minus, 5, y−5y equals= minus, 13, right parenthesis−13)
minus, 2, x−2x minus, 7, y−7y equals= minus, 14−14
minus, x−x minus, 5, y−5y equals= minus, 13−13
0
0xx plus+
0
0yy equals=
Answer
Attempt 1 out of 2
You must answer all questions above in order to submit.
Answer
no i need to fill in the blank spaces
Answered by
GPT-4o mini
To eliminate a variable in the given system of equations, you can look at the coefficients of the variables. The equations are:
1. \( 3x - 4y = 0 \)
2. \( -3x + 9y = 30 \)
To eliminate \( x \), you can add the two equations together, since the coefficients of \( x \) are opposites (\(3\) in the first and \(-3\) in the second). By adding these equations, the \( x \) terms will cancel each other out.
So, the correct first step is:
**A, d, d, to eliminate , x, . Add to eliminate x.**
1. \( 3x - 4y = 0 \)
2. \( -3x + 9y = 30 \)
To eliminate \( x \), you can add the two equations together, since the coefficients of \( x \) are opposites (\(3\) in the first and \(-3\) in the second). By adding these equations, the \( x \) terms will cancel each other out.
So, the correct first step is:
**A, d, d, to eliminate , x, . Add to eliminate x.**
Answered by
GPT-4o mini
To eliminate a variable in this system of equations, let's write out the equations clearly:
1. \( -8x - y = 35 \)
2. \( -8x - 5y = 15 \)
Both equations have the same coefficient for \( x \) (\(-8x\)). Thus, to eliminate \( x \), we can subtract one equation from the other.
The correct first step is:
**S, u, b, t, r, a, c, t, to eliminate , x, . Subtract to eliminate x.**
1. \( -8x - y = 35 \)
2. \( -8x - 5y = 15 \)
Both equations have the same coefficient for \( x \) (\(-8x\)). Thus, to eliminate \( x \), we can subtract one equation from the other.
The correct first step is:
**S, u, b, t, r, a, c, t, to eliminate , x, . Subtract to eliminate x.**
Answered by
GPT-4o mini
To solve the system of equations by combining them, we have the following equations:
1. \( -2x - 7y = -14 \)
2. \( -x - 5y = -13 \)
### Step 1: Eliminate one variable
We can eliminate the \( x \) variable by multiplying the second equation by 2, so that the coefficients of \( x \) will match (but opposite in sign):
1. First equation: \( -2x - 7y = -14 \) (no changes needed)
2. Multiply the second equation by 2:
\[
2(-x - 5y) = 2(-13)
\]
This gives us:
\[
-2x - 10y = -26
\]
### Step 2: Combine the modified equations
Now we can rewrite the equations:
1. \( -2x - 7y = -14 \)
2. \( -2x - 10y = -26 \)
Now let's subtract the first equation from the second:
\[
(-2x - 10y) - (-2x - 7y) = -26 - (-14)
\]
**Simplifying this gives:**
\[
-10y + 7y = -26 + 14
\]
This simplifies to:
\[
-3y = -12
\]
### Step 3: Solve for \( y \)
Divide both sides by -3:
\[
y = 4
\]
### Step 4: Substitute back to find \( x \)
Now that we have \( y \), we substitute \( y = 4 \) back into one of the original equations. We'll use the first equation:
\[
-2x - 7(4) = -14
\]
This simplifies to:
\[
-2x - 28 = -14
\]
Adding 28 to both sides:
\[
-2x = 14
\]
Dividing by -2 yields:
\[
x = -7
\]
### Final Solution
The solution to the system of equations is:
\[
x = -7, \quad y = 4
\]
Please note the format you might need to fill in for the input boxes:
- For coefficients:
- \( x \): -7
- \( y \): 4
- Constant: 0 (since there is no constant term in the combined equation)
### Try Button
After inputting these values into the boxes provided, you can press the "try" button to see if the solution is correct. If it is, you will get a new question.
1. \( -2x - 7y = -14 \)
2. \( -x - 5y = -13 \)
### Step 1: Eliminate one variable
We can eliminate the \( x \) variable by multiplying the second equation by 2, so that the coefficients of \( x \) will match (but opposite in sign):
1. First equation: \( -2x - 7y = -14 \) (no changes needed)
2. Multiply the second equation by 2:
\[
2(-x - 5y) = 2(-13)
\]
This gives us:
\[
-2x - 10y = -26
\]
### Step 2: Combine the modified equations
Now we can rewrite the equations:
1. \( -2x - 7y = -14 \)
2. \( -2x - 10y = -26 \)
Now let's subtract the first equation from the second:
\[
(-2x - 10y) - (-2x - 7y) = -26 - (-14)
\]
**Simplifying this gives:**
\[
-10y + 7y = -26 + 14
\]
This simplifies to:
\[
-3y = -12
\]
### Step 3: Solve for \( y \)
Divide both sides by -3:
\[
y = 4
\]
### Step 4: Substitute back to find \( x \)
Now that we have \( y \), we substitute \( y = 4 \) back into one of the original equations. We'll use the first equation:
\[
-2x - 7(4) = -14
\]
This simplifies to:
\[
-2x - 28 = -14
\]
Adding 28 to both sides:
\[
-2x = 14
\]
Dividing by -2 yields:
\[
x = -7
\]
### Final Solution
The solution to the system of equations is:
\[
x = -7, \quad y = 4
\]
Please note the format you might need to fill in for the input boxes:
- For coefficients:
- \( x \): -7
- \( y \): 4
- Constant: 0 (since there is no constant term in the combined equation)
### Try Button
After inputting these values into the boxes provided, you can press the "try" button to see if the solution is correct. If it is, you will get a new question.
Answered by
GPT-4o mini
I apologize for the misunderstanding. Let's fill in the blanks step by step based on the system of equations:
1. Original equations:
- \( -2x - 7y = -14 \)
- \( -x - 5y = -13 \)
### Step 1: Multiply the second equation by 2
We want to eliminate \( x \), so we continue processing our equations:
1. The first equation remains:
\[
-2x - 7y = -14
\]
2. The second equation multiplied by 2 is:
\[
2(-x - 5y) = 2(-13) \implies -2x - 10y = -26
\]
### Step 2: Set up for subtraction
Now we have:
- Equation 1: \( -2x - 7y = -14 \)
- Equation 2: \( -2x - 10y = -26 \)
### Step 3: Subtract the equations
Subtract the first equation from the second:
\[
(-2x - 10y) - (-2x - 7y) = -26 - (-14)
\]
This simplifies to:
\[
-10y + 7y = -26 + 14
\]
\[
-3y = -12
\]
Now we'll fill in the blanks:
1. Coefficients for \( x \): **0** (because \( x \) gets eliminated)
2. Coefficients for \( y \): **-3**
3. Constant on the right: **-12**
### Result of the subtraction:
Thus, the resulting equation from combining the two is:
\[
0x - 3y = -12
\]
### Final answer to fill in:
- For coefficient of \( x \): **0**
- For coefficient of \( y \): **-3**
- For the constant: **-12**
You are now ready to press the "try" button with these filled values. Let me know if you need any more assistance!
1. Original equations:
- \( -2x - 7y = -14 \)
- \( -x - 5y = -13 \)
### Step 1: Multiply the second equation by 2
We want to eliminate \( x \), so we continue processing our equations:
1. The first equation remains:
\[
-2x - 7y = -14
\]
2. The second equation multiplied by 2 is:
\[
2(-x - 5y) = 2(-13) \implies -2x - 10y = -26
\]
### Step 2: Set up for subtraction
Now we have:
- Equation 1: \( -2x - 7y = -14 \)
- Equation 2: \( -2x - 10y = -26 \)
### Step 3: Subtract the equations
Subtract the first equation from the second:
\[
(-2x - 10y) - (-2x - 7y) = -26 - (-14)
\]
This simplifies to:
\[
-10y + 7y = -26 + 14
\]
\[
-3y = -12
\]
Now we'll fill in the blanks:
1. Coefficients for \( x \): **0** (because \( x \) gets eliminated)
2. Coefficients for \( y \): **-3**
3. Constant on the right: **-12**
### Result of the subtraction:
Thus, the resulting equation from combining the two is:
\[
0x - 3y = -12
\]
### Final answer to fill in:
- For coefficient of \( x \): **0**
- For coefficient of \( y \): **-3**
- For the constant: **-12**
You are now ready to press the "try" button with these filled values. Let me know if you need any more assistance!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.