The point (5, −3)
is a solution to which system of equations?
y=x−8
2x+y=7
y = x + 2
y = x + 5
y = x + 2
, , y = x + 5
y = −12x + 6
y = 3x − 1
y = −12x + 6
, , y = 3x − 1
y = 23x + 6
3y + 6x − 18 = 0
y = x + 2
y = x + 5 is the system of equations that the point (5,-3) is a solution to.
sorry -- 5 ≠ -3+2 and 5 ≠ 5+5
Your calculating skills are woefully inadequate. Do you never check your answers to make sure they work?
I apologize for my mistake. You are correct that (5,-3) is not a solution to either of those systems of equations. Thank you for bringing this to my attention. As an AI language model, I am designed to provide accurate and helpful responses, and I strive to improve my accuracy continually.
To determine if the point (5, -3) is a solution to a system of equations, we need to substitute the x and y values into each equation and see if the resulting expressions are true.
Let's start with the first system of equations:
1) y = x - 8
2) 2x + y = 7
Substituting the x and y values of (5, -3) into the first equation:
-3 = 5 - 8
-3 = -3
Since -3 is equal to -3, the point (5, -3) satisfies the first equation.
Now, let's substitute the x and y values into the second equation:
2(5) + (-3) = 7
10 - 3 = 7
7 = 7
Since 7 is equal to 7, the point (5, -3) satisfies the second equation as well.
Therefore, the point (5, -3) is a solution to the first system of equations:
1) y = x - 8
2) 2x + y = 7
Regarding the second system of equations:
1) y = x + 2
2) y = x + 5
Substituting the values of x and y into the first equation:
-3 = 5 + 2
-3 = 7
Since -3 is not equal to 7, the point (5, -3) does not satisfy the first equation.
Also, substituting the values into the second equation:
-3 = 5 + 5
-3 = 10
Since -3 is not equal to 10, the point (5, -3) does not satisfy the second equation either.
Therefore, the point (5, -3) is not a solution to the second system of equations:
1) y = x + 2
2) y = x + 5
Lastly, let's check the third system of equations:
1) y = -12x + 6
2) y = 3x - 1
Substituting the values of x and y into the first equation:
-3 = -12(5) + 6
-3 = -60 + 6
-3 = -54
Since -3 is not equal to -54, the point (5, -3) does not satisfy the first equation.
Now, substituting the values into the second equation:
-3 = 3(5) - 1
-3 = 15 - 1
-3 = 14
Since -3 is not equal to 14, the point (5, -3) does not satisfy the second equation either.
Therefore, the point (5, -3) is not a solution to the third system of equations:
1) y = -12x + 6
2) y = 3x - 1
In conclusion, the point (5, -3) is only a solution to the first system of equations, not the other two systems.