Which of the following shows the equation that creates a true equivalent system?
System A -x=y=1 and x+y= 11 System B x+y=11 ?
−x−y=−1 negative x minus y equals negative 1 2y=12 2 y equals 12 −2x−2y=−22 negative 2 x minus 2 y equals negative 22 2x+2y=12
System A: -x=y=1 and x+y=11
System B: -x-y=-1, 2y=12, -2x-2y=-22, 2x+2y=12
The equation that creates a true equivalent system is -x-y=-1.
Use the table to answer the question. System A 7x+4y=−4 and 5x+8y=28 System B 7x+4y=−4 ? Which of the following terms will make the systems equivalent?
−14x−8y=−8 negative 14 x minus 8 equals negative 8 12x+12y=24 12 x plus 12 y equals 24 −12x−12y=24 negative 12 x minus 12 y equals 24 −14x−8y=8
System A: 7x+4y=-4 and 5x+8y=28
System B: 7x+4y=-4, ?,
To make the systems equivalent, we need to find an equation in System B that is equivalent to the second equation in System A, 5x+8y=28.
The equation that makes the systems equivalent is 5x+8y=28.
Pick an option
Based on the options provided, the equation that makes the systems equivalent is 12x+12y=24.
Use the elimination method to solve the linear-quadratic system y=x^2+10 , y=−7x−2.
To solve the system using the elimination method, we need to eliminate one variable by manipulating the equations to create a system of linear equations.
The given equations are:
y = x^2 + 10 (Equation 1)
y = -7x - 2 (Equation 2)
To eliminate the variable "y", we can set the right sides of the equations equal to each other:
x^2 + 10 = -7x - 2
Now, let's bring all the terms to one side:
x^2 + 7x + 12 = 0
This is a quadratic equation. We can factor it:
(x + 3)(x + 4) = 0
Setting each factor equal to zero, we get:
x + 3 = 0 or x + 4 = 0
Solving for "x", we get:
x = -3 or x = -4
Now, substitute these values of "x" into one of the equations to find the corresponding values of "y". Let's use Equation 1:
For x = -3:
y = (-3)^2 + 10
y = 9 + 10
y = 19
For x = -4:
y = (-4)^2 + 10
y = 16 + 10
y = 26
Therefore, the solutions to the system are (-3, 19) and (-4, 26).
Use the elimination method to solve the linear-quadratic system y=x^2+10 , y=−7x−2 .
To solve the system using the elimination method, we can set the right sides of the equations equal to each other:
x^2 + 10 = -7x - 2
Rearranging the equation, we get:
x^2 + 7x + 12 = 0
Now, we can factor the quadratic equation:
(x + 3)(x + 4) = 0
Setting each factor equal to zero, we find:
x + 3 = 0 or x + 4 = 0
Solving for x, we obtain:
x = -3 or x = -4
Now, substitute these values of x into one of the original equations to find the corresponding values of y. Let's use the equation y = x^2 + 10:
For x = -3:
y = (-3)^2 + 10
y = 9 + 10
y = 19
For x = -4:
y = (-4)^2 + 10
y = 16 + 10
y = 26
Therefore, the solutions to the system are (-3, 19) and (-4, 26).