Which point would be a solution to the system of linear inequalities shown below?
y, is less than or equal to, minus, one fifth, x, minus, 8, y, is greater than or equal to, 5, x, plus, 5
y≤−
5
1
x−8y≥5x+5
Answer
Multiple Choice Answers
left parenthesis, minus, 5, comma, 3, right parenthesis(−5,3)
left parenthesis, minus, 10, comma, 5, right parenthesis(−10,5)
left parenthesis, minus, 10, comma, minus, 6, right parenthesis(−10,−6)
left parenthesis, minus, 5, comma, 2, right parenthesis(−5,2)
11 answers
To determine which point is a solution to the system of inequalities, we need to test each point in the inequalities given:
Inequality 1:
Inequality 2:
Let's evaluate each point:
Point 1:
For :
This point does not satisfy the first inequality.
Point 2:
For :
This point does not satisfy the first inequality.
Point 3:
For :
For :
This point satisfies both inequalities.
Point 4:
For :
This point does not satisfy the first inequality.
Conclusion:
The only point that satisfies both inequalities is .
Thus, the solution to the system of inequalities is
Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities.
y, is greater than, minus, one half, x, minus, 2
y>−
2
1
x−2
y, is greater than, x, plus, 1
y>x+1
x
y
Answer
Multiple Choice Answers
left parenthesis, minus, 6, comma, minus, 4, right parenthesis(−6,−4)
left parenthesis, minus, 2, comma, 1, right parenthesis(−2,1)
left parenthesis, 8, comma, 8, right parenthesis(8,8)
left parenthesis, 0, comma, minus, 7, right parenthesis(0,−7)
To determine which point satisfies both inequalities, we need to analyze each inequality and see where the solution regions are located:
Inequality 1:
Inequality 2:
Step 1: Determine the regions for each inequality
For the first inequality, the line has a downward slope and y-intercept of -2. The region satisfying this inequality is above this line.
For the second inequality, the line has an upward slope of 1 and y-intercept of 1. The region satisfying this inequality is also above this line.
Step 2: Verify each point
Now, we will substitute each point into both inequalities to see if they satisfy both conditions.
Point 1:
For :
For :
Point does not satisfy the first inequality.
Point 2:
For :
For :
Point satisfies both inequalities.
Point 3:
For :
For :
Point does not satisfy the second inequality.
Point 4:
For :
For :
Point does not satisfy either inequality.
Conclusion
The only point that satisfies both inequalities is .
Thus, the solution is:
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
5, x, plus, y, equals, 48
5x+y=
48
3, x, minus, y, equals, 16
3x−y=
16
Answer
Multiple Choice Answers
A, d, d, to eliminate , y, .Add to eliminate y.
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 , x, .Add to eliminate x.
To solve the system of equations
we can choose to eliminate either variable or . Let's analyze the options:
Option A: "Add to eliminate ."
If we add the two equations, the terms would cancel out because appears as in the first equation and in the second equation.
Option B: "Subtract to eliminate ."
If we were to subtract the first equation from the second (or vice versa), the terms would not cancel out nicely because they both involve with different coefficients. This is not the correct approach for eliminating .
Option C: "Subtract to eliminate ."
If we were to subtract the second equation from the first, we wouldn't eliminate because the signs in front of in the equations are and . This would not give us a cancellation.
Option D: "Add to eliminate ."
Adding the equations would not eliminate as both equations have different coefficients for .
Conclusion
The correct first step is:
Add to eliminate (Option A).
Thus, the answer is:
nd the solution of the system of equations.
minus, 10, x, minus, y, equals, minus, 29
−10x−y=
−29
10, x, plus, 7, y, equals, 23
10x+7y=
23
Answer
Attempt 1 out of 2
left parenthesis(
,
right parenthesis) Submit Answer
To solve the system of equations
we can use the method of elimination or substitution. Here, we'll use the elimination method.
Step 1: Eliminate
From equation (1), we can express in terms of :
Step 2: Substitute into the second equation
Now, we will substitute equation (3) into equation (2):
Step 3: Solve for
Now, isolate :
Step 4: Substitute back to find
Now, substitute back into equation (3):
Conclusion
The solution to the system of equations is:
So, the final answer is:
or
Please choose the format that’s preferred based on your submission requirements.
Find the solution of the system of equations.
minus, 2, x, minus, 2, y, equals, 0
−2x−2y=
0
minus, x, plus, 4, y, equals, 40
−x+4y=
40
To solve the system of equations
we can simplify and solve them step by step.
Step 1: Simplify Equation (1)
From equation (1), we can simplify it:
This means
Step 2: Substitute Equation (3) into Equation (2)
Now, we'll substitute equation (3) into equation (2):
Step 3: Solve for
Now we will solve for :
Step 4: Substitute back to find
Now we can substitute back into equation (3) to find :
Conclusion
The solution to the system of equations is:
So the final answer is .
Solve the system by substitution.
y, equals, 3, x, plus, 14
y=
3x+14
y, equals, x
y=
x
To solve the system of equations using substitution, we have:
\quad (1)
\quad (2)
Step 1: Substitute Equation (2) into Equation (1)
Since both equations are equal to , we can set them equal to each other:
Step 2: Solve for
Now, we will isolate :
Step 3: Substitute back into either equation to find
Now that we have found , we can substitute back into equation (2):