so wat do u mean by that
WHICH ORDERED PAIR IS A SOLUTION OF THE FOLLOWING SYSTEM OF LINEAR EQUATION
2X-5Y=NEGATIVE 12
NEGATIVEX +4Y=9
A{NEGATIVE6,0}
B{3,3}
C{NEGATIVE1,2}
D{2,2}
I will be happy to critique your thinking on this.
I mean I wont do your homework/tests for you, but will be glad to check your work.
http://www.askoxford.com/concise_oed/critique?view=uk
how to solve linear equations
its b
To solve a system of linear equations, we need to find the values of x and y that satisfy both equations simultaneously. Here's how you can solve the given system of equations:
Step 1: Start with the first equation: 2x - 5y = -12.
Step 2: Simplify the equation if needed. In this case, it is already simplified.
Step 3: Solve the equation for one variable in terms of the other. Let's solve it for x:
2x = 5y - 12
x = (5y - 12)/2 = 2.5y - 6
Step 4: Move on to the second equation: -x + 4y = 9.
Step 5: Simplify the equation if needed. In this case, it is already simplified.
Step 6: Solve the equation for one variable in terms of the other. Let's solve it for x:
-x = -4y + 9
x = 4y - 9
Step 7: Now we have two expressions for x in terms of y. Set them equal to each other and solve for y:
2.5y - 6 = 4y - 9
Step 8: Simplify and solve for y:
1.5 = 1.5y
y = 1
Step 9: Substitute the value of y = 1 into either of the original equations to solve for x:
2x - 5(1) = -12
2x - 5 = -12
2x = -12 + 5
2x = -7
x = -3.5
Therefore, the solution to the system of linear equations is x = -3.5 and y = 1.
Now let's check which ordered pair is a solution to the given system:
A{ -6, 0 }:
2(-6) - 5(0) = -12
-12 - 0 = -12 (Correct)
-(-6) + 4(0) = 9
6 + 0 = 9 (Incorrect)
B{ 3, 3 }:
2(3) - 5(3) = -12
6 - 15 = -12 (Incorrect)
-(3) + 4(3) = 9
-3 + 12 = 9 (Correct)
C{ -1, 2 }:
2(-1) - 5(2) = -12
-2 - 10 = -12 (Correct)
-(-1) + 4(2) = 9
1 + 8 = 9 (Correct)
D{ 2, 2 }:
2(2) - 5(2) = -12
4 - 10 = -12 (Incorrect)
-(2) + 4(2) = 9
-2 + 8 = 9 (Correct)
Therefore, the ordered pair C{ -1, 2 } is a solution to the given system of linear equations.
To solve a system of linear equations, you can use the method of substitution or elimination. Let's go through the steps to solve the given system of linear equations:
The given system of equations is:
1) 2x - 5y = -12
2) -x + 4y = 9
We can solve this system using the substitution method:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve equation 2) for x:
-x + 4y = 9
Add x to both sides:
4y = x + 9
Divide both sides by 4:
y = (1/4)x + (9/4)
Step 2: Substitute the expression found in Step 1 back into the other equation.
Substitute (1/4)x + (9/4) for y in equation 1):
2x - 5((1/4)x + (9/4)) = -12
Step 3: Simplify and solve for x.
2x - (5/4)x - (45/4) = -12
Multiplying through by 4 to eliminate the fraction:
8x - 5x - 45 = -48
Combine like terms:
3x - 45 = -48
Add 45 to both sides:
3x = -3
Divide both sides by 3:
x = -1
Step 4: Substitute the value of x back into one of the original equations and solve for y.
Using equation 2):
-x + 4y = 9
-(-1) + 4y = 9
1 + 4y = 9
Subtract 1 from both sides:
4y = 8
Divide both sides by 4:
y = 2
So, the solution to the system of linear equations is (x, y) = (-1, 2).
Now, let's check which ordered pair is a solution to the system of equations:
A) (-6, 0):
Substituting these values into the equations:
1) 2(-6) - 5(0) = -12 --> -12 - 0 = -12 (True)
2) -(-6) + 4(0) = 9 --> 6 + 0 = 9 (False)
B) (3, 3):
Substituting these values into the equations:
1) 2(3) - 5(3) = -12 --> 6 - 15 = -12 (False)
2) -(3) + 4(3) = 9 --> -3 + 12 = 9 (True)
C) (-1, 2):
Substituting these values into the equations:
1) 2(-1) - 5(2) = -12 --> -2 - 10 = -12 (False)
2) -(-1) + 4(2) = 9 --> 1 + 8 = 9 (True)
D) (2, 2):
Substituting these values into the equations:
1) 2(2) - 5(2) = -12 --> 4 - 10 = -12 (False)
2) -(2) + 4(2) = 9 --> -2 + 8 = 9 (False)
From the above calculations, we can see that the ordered pair C) (-1, 2) is the solution to the given system of linear equations.