Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations: 8x−2y=−4 4x−y=−2 (2 points) Responses Solve this system by elimination since it is already in standard form and lined up nicely. There is exactly one solution to this system of linear equations and it is (2, 0). There are infinite solutions to this system of linear equations. . These lines are parallel, so there is no solution to this system of linear equations. There is exactly one solution to this system of linear equations and it is (0, -2). Solve this system by substitution since one of the variables is defined by the other without having to do any math
My apologies for the confusion. In that case, the correct statements that describe the solution to this system of equations are:
- There are infinite solutions to this system of linear equations.
- These lines are parallel, so there is no solution to this system of linear equations.
The statement "These lines are parallel, so there is no solution to this system of linear equations" correctly describes the solution to this system.
To check which statement(s) correctly describe the solution to the given system of equations, let's solve the system step-by-step.
The system of equations is:
8x - 2y = -4 ...(equation 1)
4x - y = -2 ...(equation 2)
To solve the system by elimination, we can multiply equation 2 by 2 and add it to equation 1 to eliminate the y variable. Let's perform this step:
2 * (4x - y) = 2 * (-2)
8x - 2y = -4 ...(equation 1)
8x - 2y = -4 ...(equation 2 after multiplication)
Now, if we subtract equation 2 from equation 1, we get:
(8x - 2y) - (8x - 2y) = (-4) - (-4)
Simplifying this further:
0 = 0
Since this equation is always true, it means that the two equations are equivalent and represent the same line. Therefore, the lines are coincident and have an infinite number of solutions.
So, the correct response is: There are infinite solutions to this system of linear equations.
To determine the correct statement(s) that describe the solution to the given system of equations, let's start by understanding the methods used to solve systems of linear equations.
Option 1: Solve by elimination method - This involves manipulating the equations to eliminate one variable by adding or subtracting the equations. Once one variable is eliminated, the system can be solved for the remaining variable.
Option 2: Solve by substitution method - This method involves solving one equation for one variable and substituting the expression into the other equation. This reduces the system to one equation with one variable, which can then be solved.
Let's apply these methods to the given system of equations:
Equation 1: 8x - 2y = -4
Equation 2: 4x - y = -2
Using elimination method:
To eliminate the y variable, we can multiply Equation 2 by 2, making the coefficients of y equal in both equations:
2(4x - y) = 2(-2) => 8x - 2y = -4
We can see that Equation 1 is a multiple of Equation 2, which means they represent the same line. Therefore, these equations are dependent, and there are infinite solutions to this system of equations.
Using substitution method:
Solving Equation 2 for y, we get:
y = 4x + 2
Now, substitute this expression for y into Equation 1:
8x - 2(4x + 2) = -4
Simplifying this equation gives:
8x - 8x - 4 = -4
-4 = -4
This equation is true. As a result, there are infinite solutions to this system of equations.
Based on these calculations, the correct statement(s) that describe the solution to the system of equations are:
- There are infinite solutions to this system of linear equations.
its a multy ansewr questiion which ones r irght
You are running a concession stand at a baseball game. You are selling pizza slices and sodas. Each pizza slice sells for $3.50 and each soda sells for $1.50. At the end of the night, you made a total of $800. You sold a total of 344 pizza slices and sodas combined. You must report the number of pizza slices sold and the number of sodas sold. What equations did you use to solve this, where P = the number of pizza slices sold and S = the number of sodas sold? (1 point) Responses 3.50P + 1.50S = 800 and P + S = 344 3.50P + 1.50S = 800 and P + S = 344 3.50P + S = 800 and P + 1.50S = 344 3.50P + S = 800 and P + 1.50S = 344 3.50S + 1.50P = 800 and P + S = 344 3.50S + 1.50P = 800 and P + S = 344 3.50S + 1.50P = 344 and P + S = 800
The equations used to solve this problem are:
3.50P + 1.50S = 800 (equation for the total amount of money made)
P + S = 344 (equation for the total number of pizza slices and sodas sold)