To solve this system of equations, we can use substitution or elimination method. Let's use substitution method:
From the first equation, we have y = x - 8. Substituting this into the second equation:
2x + (x - 8) = 7
3x - 8 = 7
3x = 7 + 8
3x = 15
x = 15/3
x = 5
Substituting the value of x into the first equation to find y:
y = 5 - 8
y = -3
Therefore, the solution to the system of equations is x = 5 and y = -3.
y\ =\ x\ -\ 8\ 2x\ +\ y\ =\ 7
9 answers
y=−2x+12 4y+x−20=0
To solve the system of equations, we can use the substitution method or elimination method. Let's use substitution:
From the first equation, we have y = -2x + 12. Substituting this into the second equation:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = -28 / -7
x = 4
Substituting the value of x into the first equation to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
Therefore, the solution to the system of equations is x = 4 and y = 4.
From the first equation, we have y = -2x + 12. Substituting this into the second equation:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = -28 / -7
x = 4
Substituting the value of x into the first equation to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
Therefore, the solution to the system of equations is x = 4 and y = 4.
how many solutions does it have?
To determine the number of solutions, we can analyze the system of equations.
The first equation, y = -2x + 12, represents a straight line. Since it has a slope of -2, the line is descending (negative slope). This equation represents a linear equation with infinite solutions.
The second equation, 4y + x - 20 = 0, represents another straight line. This equation is not equivalent to the first equation, so they are not the same line. Since it is also a linear equation, it will have infinite solutions.
Therefore, the system of equations has infinitely many solutions.
The first equation, y = -2x + 12, represents a straight line. Since it has a slope of -2, the line is descending (negative slope). This equation represents a linear equation with infinite solutions.
The second equation, 4y + x - 20 = 0, represents another straight line. This equation is not equivalent to the first equation, so they are not the same line. Since it is also a linear equation, it will have infinite solutions.
Therefore, the system of equations has infinitely many solutions.
Are you sure?
Apologies for the confusion. You're right, I misspoke in my previous response.
To determine the number of solutions for the system of equations, we need to consider whether the lines represented by the equations intersect or are parallel.
Let's rearrange the second equation to make it easier to analyze:
4y + x - 20 =0
4y = -x + 20
y = (-1/4)x + 5
Now, we have the two equations:
y = -2x + 12
y = (-1/4)x + 5
We can see that the slopes of the two lines are different: -2 and -1/4. Therefore, the lines are not parallel.
Since the lines are not parallel and have different slopes, they will intersect at a particular point. Hence, the system of equations will have a single unique solution.
Apologies for my earlier mistake, and thank you for pointing it out.
To determine the number of solutions for the system of equations, we need to consider whether the lines represented by the equations intersect or are parallel.
Let's rearrange the second equation to make it easier to analyze:
4y + x - 20 =0
4y = -x + 20
y = (-1/4)x + 5
Now, we have the two equations:
y = -2x + 12
y = (-1/4)x + 5
We can see that the slopes of the two lines are different: -2 and -1/4. Therefore, the lines are not parallel.
Since the lines are not parallel and have different slopes, they will intersect at a particular point. Hence, the system of equations will have a single unique solution.
Apologies for my earlier mistake, and thank you for pointing it out.
so what is the solution?
To find the solution, we will substitute the value of y from the first equation into the second equation:
y = -2x + 12
Substituting this into the second equation:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = -28 / -7
x = 4
Now, substitute the value of x back into the first equation to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
Therefore, the solution to the system of equations is x = 4 and y = 4.
y = -2x + 12
Substituting this into the second equation:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = -28 / -7
x = 4
Now, substitute the value of x back into the first equation to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
Therefore, the solution to the system of equations is x = 4 and y = 4.