Which equation describes an infinite solution system with the equation y=4x−3?
−2y+8x=−6 negative 2 y plus 8 x equals negative 6 2y+8x=−6 2 y plus 8 x equals negative 6 2y−8x=−6 2 y minus 8 x equals negative 6 2y−8x=6
The equation that describes an infinite solution system with the equation y = 4x - 3 is 2y - 8x = 6.
What is the solution of y=2x−1 and y−3=4x ? (1 point)
To find the solution of the system of equations y = 2x - 1 and y - 3 = 4x, we can use the substitution method.
1. Rearrange the second equation to solve for y:
y = 4x + 3
2. Substitute the expression for y in the first equation:
2x - 1 = 4x + 3
3. Simplify the equation by combining like terms:
-2x = 4
4. Divide both sides of the equation by -2:
x = -2
5. Substitute the value of x back into either equation to find the value of y:
y = 2(-2) - 1
y = -4 - 1
y = -5
Therefore, the solution to the system of equations y = 2x - 1 and y - 3 = 4x is x = -2 and y = -5.
Use the table to answer the question. x-value y-value if y=x+6 y-value if y=2x+3 0 6 3 1 7 5 2 8 7 3 9 9 4 10 11 A system of equations is displayed in the table. What is the solution for the system?
Looking at the table, we have two equations:
y = x + 6 ----- (Equation 1)
y = 2x + 3 ----- (Equation 2)
By comparing Equation 1 and Equation 2, we can see that they have the same y-values for each corresponding x-value in the table, except for x = 0.
For x = 0, Equation 1 gives y = 6, while Equation 2 gives y = 3. Therefore, the two equations do not have the same solution for x = 0.
Since there is no consistent solution for the system of equations in the table, we can say that the system is inconsistent.
To determine which equation describes an infinite solution system with the given equation y = 4x - 3, we can compare the coefficients and constants of the equations.
In the given equation y = 4x - 3, the coefficient of x is 4, and the coefficient of y is 1. The constant term is -3.
Let's analyze each of the options:
1. -2y + 8x = -6: The coefficient of x is 8, and the coefficient of y is -2. This equation does not have the same coefficients as the given equation, so it does not describe an infinite solution system.
2. 2y + 8x = -6: The coefficient of x is 8, and the coefficient of y is 2. This equation does not have the same coefficients as the given equation, so it does not describe an infinite solution system.
3. 2y - 8x = -6: The coefficient of x is -8, and the coefficient of y is 2. This equation does not have the same coefficients as the given equation, so it does not describe an infinite solution system.
4. 2y - 8x = 6: The coefficient of x is -8, and the coefficient of y is 2. This equation has the same coefficients as the given equation (just with opposite signs). Therefore, this equation describes an infinite solution system.
So the equation that describes an infinite solution system with the given equation y = 4x - 3 is 2y - 8x = 6.