Hi! Can someone check my answers? Thanks!
Directions: Solve each system by using the elimination method. Make sure to write your answer in (x,y) form.
1.) 3x-5y=2
2x+5y=13
2.) 3x+11y=4
-2x-5y=9
My answers:
1.) (3,7/5)
2.) (-17,5)
Right!
Hello! I can help you check your answers for the given systems of equations.
Let's start by verifying your answer for the first system:
1.) 3x - 5y = 2
2x + 5y = 13
To solve this system using the elimination method, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can add the two equations together to eliminate the "y" variable:
(3x - 5y) + (2x + 5y) = 2 + 13
3x + 2x + (-5y + 5y) = 15
5x = 15
x = 15/5
x = 3
Now that we have the value of "x," we can substitute it back into one of the original equations to solve for "y." Let's use the first equation:
3x - 5y = 2
3(3) - 5y = 2
9 - 5y = 2
-5y = 2 - 9
-5y = -7
y = (-7)/(-5)
y = 7/5
So the solution to the first system of equations is (x, y) = (3, 7/5).
Now let's move on to the second system:
2.) 3x + 11y = 4
-2x - 5y = 9
Similarly, we'll eliminate one of the variables, and in this case, we can eliminate the "x" variable by multiplying the second equation by 3 and the first equation by -2:
(-2)(3x + 11y) = (-2)(4)
(3)(-2x - 5y) = (3)(9)
-6x - 22y = -8
-6x - 15y = 27
Now we can subtract the second equation from the first equation to eliminate the "x" variable:
(-6x - 22y) - (-6x - 15y) = -8 - 27
-6x - 22y + 6x + 15y = -35
-7y = -35
y = (-35)/(-7)
y = 5
Now that we have the value of "y," we can substitute it back into one of the original equations to solve for "x." Let's use the first equation:
3x + 11y = 4
3x + 11(5) = 4
3x + 55 = 4
3x = 4 - 55
3x = -51
x = (-51)/3
x = -17
So the solution to the second system of equations is (x, y) = (-17, 5).
Great job on your answers! They are correct:
1.) (3, 7/5)
2.) (-17, 5)
If you have any more questions or need further clarification, feel free to ask!