Question
Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .
no solution no solution (2−1) left parenthesis 2 comma negative 1 right parenthesis infinite solutions infinite solutions (−1,2)
no solution no solution (2−1) left parenthesis 2 comma negative 1 right parenthesis infinite solutions infinite solutions (−1,2)
Answers
Answer
Use the substitution method to solve the system x=y−4, x+8y=2.
(−313,23) left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis no solution no solution infinite solutions infinite solutions (23,−313)
(−313,23) left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis no solution no solution infinite solutions infinite solutions (23,−313)
Answer
Use the substitution method to solve the system x=y−4, x+8y=2.
(−3 1/3,2/3) left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis no solution no solution infinite solutions infinite solutions (2/3,−3 1/3)
(−3 1/3,2/3) left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis no solution no solution infinite solutions infinite solutions (2/3,−3 1/3)
Answer
Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .
no solution no solution (−2,3) left parenthesis negative 2 comma 3 right parenthesis infinite solutions infinite solutions (3,−2) left parenthesis 3 comma negative 2 right parenthesis
no solution no solution (−2,3) left parenthesis negative 2 comma 3 right parenthesis infinite solutions infinite solutions (3,−2) left parenthesis 3 comma negative 2 right parenthesis
Answer
Which of the followin(4,8) and (3,5) left parenthesis 4 comma 8 right parenthesis and left parenthesis 3 comma 5 right parenthesis (4,8) left parenthesis 4 comma 8 right parenthesis (3,5) left parenthesis 3 comma 5 right parenthesis (−4,−16) and (−3,−13)g uses the substitution method to solve linear-quadratic system y=x^2−4x+8 , y=3x−4 ?(
Answered by
GPT 3.5
To solve the system using the substitution method, we first solve one of the equations for one variable in terms of the other variable, and then substitute this expression into the other equation.
From the first equation, we can solve for x in terms of y:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y) / 2
Now, we substitute this expression for x into the second equation:
-4x - 6y = -8
-4((4 - 3y) / 2) - 6y = -8
-2(4 - 3y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8
This equation simplifies to -8 = -8. Since this equation is always true, it implies that the system has infinite solutions.
Therefore, the correct answer is: infinite solutions.
From the first equation, we can solve for x in terms of y:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y) / 2
Now, we substitute this expression for x into the second equation:
-4x - 6y = -8
-4((4 - 3y) / 2) - 6y = -8
-2(4 - 3y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8
This equation simplifies to -8 = -8. Since this equation is always true, it implies that the system has infinite solutions.
Therefore, the correct answer is: infinite solutions.
Answered by
GPT 3.5
To solve the system using the substitution method, we first solve one of the equations for one variable in terms of the other variable, and then substitute this expression into the other equation.
From the first equation, we can solve for x in terms of y:
x = y - 4
Now, we substitute this expression for x into the second equation:
(y - 4) + 8y = 2
9y - 4 = 2
9y = 6
y = 6/9
y = 2/3
Now that we have found the value of y, we can substitute it back into the first equation to find x:
x = (2/3) - 4
x = -12/3 - 4
x = -4 - 4
x = -8
Therefore, the solution to the system of equations is (-8, 2/3), which can also be written as (-313, 23) in fraction form.
The correct answer is: (-313, 23).
From the first equation, we can solve for x in terms of y:
x = y - 4
Now, we substitute this expression for x into the second equation:
(y - 4) + 8y = 2
9y - 4 = 2
9y = 6
y = 6/9
y = 2/3
Now that we have found the value of y, we can substitute it back into the first equation to find x:
x = (2/3) - 4
x = -12/3 - 4
x = -4 - 4
x = -8
Therefore, the solution to the system of equations is (-8, 2/3), which can also be written as (-313, 23) in fraction form.
The correct answer is: (-313, 23).
Answered by
GPT 3.5
To solve the system using the substitution method, we first solve one of the equations for one variable in terms of the other variable, and then substitute this expression into the other equation.
From the first equation, we can solve for x in terms of y:
x = y - 4
Now, we substitute this expression for x into the second equation:
(y - 4) + 8y = 2
9y - 4 = 2
9y = 6
y = 6/9
y = 2/3
Now that we have found the value of y, we can substitute it back into the first equation to find x:
x = (2/3) - 4
x = -12/3 - 4
x = -4 - 4
x = -8
Therefore, the solution to the system of equations is (-8, 2/3), which can also be written as (-3 1/3, 2/3) in mixed fraction form.
The correct answer is: (-3 1/3, 2/3).
From the first equation, we can solve for x in terms of y:
x = y - 4
Now, we substitute this expression for x into the second equation:
(y - 4) + 8y = 2
9y - 4 = 2
9y = 6
y = 6/9
y = 2/3
Now that we have found the value of y, we can substitute it back into the first equation to find x:
x = (2/3) - 4
x = -12/3 - 4
x = -4 - 4
x = -8
Therefore, the solution to the system of equations is (-8, 2/3), which can also be written as (-3 1/3, 2/3) in mixed fraction form.
The correct answer is: (-3 1/3, 2/3).
Answered by
GPT 3.5
To solve the system using the substitution method, we first solve one of the equations for one variable in terms of the other variable, and then substitute this expression into the other equation.
From the first equation, we can solve for y in terms of x:
y = -2.5x - 2
Now, we substitute this expression for y into the second equation:
3x + 2(-2.5x - 2) = 0
3x - 5x - 4 = 0
-2x - 4 = 0
-2x = 4
x = 4/(-2)
x = -2
Now that we have found the value of x, we can substitute it back into the first equation to find y:
y = -2.5(-2) - 2
y = 5 - 2
y = 3
Therefore, the solution to the system of equations is (-2, 3).
The correct answer is: (-2, 3).
From the first equation, we can solve for y in terms of x:
y = -2.5x - 2
Now, we substitute this expression for y into the second equation:
3x + 2(-2.5x - 2) = 0
3x - 5x - 4 = 0
-2x - 4 = 0
-2x = 4
x = 4/(-2)
x = -2
Now that we have found the value of x, we can substitute it back into the first equation to find y:
y = -2.5(-2) - 2
y = 5 - 2
y = 3
Therefore, the solution to the system of equations is (-2, 3).
The correct answer is: (-2, 3).
Answered by
GPT 3.5
To determine which solution uses the substitution method, we need to substitute one equation into the other and check if the coordinates satisfy both equations.
Let's substitute y = 3x - 4 into the equation y = x^2 - 4x + 8:
x^2 - 4x + 8 = 3x - 4
Rearranging the equation:
x^2 - 4x - 3x + 8 + 4 = 0
x^2 - 7x + 12 = 0
Factoring the quadratic equation:
(x - 3)(x - 4) = 0
This means that x = 3 or x = 4.
Now, let's substitute these x-values back into y = 3x - 4:
For x = 3:
y = 3(3) - 4
y = 9 - 4
y = 5
For x = 4:
y = 3(4) - 4
y = 12 - 4
y = 8
The two coordinates that satisfy both equations are (3, 5) and (4, 8).
Therefore, the correct answer is: (3, 5) and (4, 8).
Let's substitute y = 3x - 4 into the equation y = x^2 - 4x + 8:
x^2 - 4x + 8 = 3x - 4
Rearranging the equation:
x^2 - 4x - 3x + 8 + 4 = 0
x^2 - 7x + 12 = 0
Factoring the quadratic equation:
(x - 3)(x - 4) = 0
This means that x = 3 or x = 4.
Now, let's substitute these x-values back into y = 3x - 4:
For x = 3:
y = 3(3) - 4
y = 9 - 4
y = 5
For x = 4:
y = 3(4) - 4
y = 12 - 4
y = 8
The two coordinates that satisfy both equations are (3, 5) and (4, 8).
Therefore, the correct answer is: (3, 5) and (4, 8).
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