1x Solve the system of equations using elimination.
8x + 7y = -16
10x + 7y = -6
A
B
C
D
E
(3,6)
(8,5)
(7,10)
(5, -8)
(-5, -8)
To solve the system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the two equations.
In this case, we can eliminate the y variable by subtracting the two equations.
(10x + 7y) - (8x + 7y) = -6 - (-16)
2x = 10
x = 5
Now, substitute the value of x into one of the original equations to find the value of y. Let's use the first equation:
8x + 7y = -16
8(5) + 7y = -16
40 + 7y = -16
7y = -56
y = -8
So the solution to the system of equations is (x, y) = (5, -8).
The correct answer is D) (5, -8).
To solve the system of equations using elimination, we will eliminate one variable by manipulating the equations. Let's start by eliminating the variable y.
First, we'll multiply the first equation by 10 and the second equation by 8 to create opposite coefficients for y.
10(8x + 7y) = 10(-16)
8(10x + 7y) = 8(-6)
This gives us:
80x + 70y = -160
80x + 56y = -48
Now, subtracting the second equation from the first equation will eliminate the variable x:
(80x + 70y) - (80x + 56y) = -160 - (-48)
Simplifying, we get:
80x - 80x + 70y - 56y = -160 + 48
14y = -112
Next, divide both sides of the equation by 14 to solve for y:
14y/14 = -112/14
y = -8
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:
8x + 7(-8) = -16
8x - 56 = -16
8x = -16 + 56
8x = 40
x = 40/8
x = 5
Therefore, the solution to the given system of equations is (x, y) = (5, -8).
Looking at the answer choices, we can see that the correct solution is (5, -8), which matches with option D.
To solve the system of equations using elimination, we need to eliminate one of the variables by manipulating the equations. In this case, we can eliminate the variable "y".
Let's start by multiplying the first equation by 10 and the second equation by 8 to make the coefficients of "y" equal.
10(8x + 7y) = 10(-16)
8(10x + 7y) = 8(-6)
This simplifies the equations to:
80x + 70y = -160
80x + 56y = -48
Now, subtract the second equation from the first equation:
(80x + 70y) - (80x + 56y) = -160 - (-48)
This simplifies to:
14y = -112
Divide both sides of the equation by 14 to solve for y:
y = -112/14
y = -8
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:
8x + 7y = -16
Substituting y = -8, we get:
8x + 7(-8) = -16
Simplifying:
8x - 56 = -16
Add 56 to both sides:
8x = 40
Divide both sides by 8 to solve for x:
x = 40/8
x = 5
Therefore, the solution to the system of equations is (x, y) = (5, -8).
So, the correct answer is option D) (5, -8).