Equation A: 3x+y=23
Equation B: 4x−y=12
Use the system of equations to determine which of the following statements are true. Select all that apply.
The solution to the system of equations is (5,8)
The solution to the system of equations is open paren 5 comma 8 close paren
(2,−4)
is a solution to neither Equation
open paren 2 comma negative 4 close paren is a solution to neither Equation
The y-intercept of Equation B is (0,12)
The y-intercept of Equation B is open paren 0 comma 12 close paren
The slope of Equation A is m = −3
The slope of Equation A is m = negative 3
(2,−4)
is a solution to Equation B
open paren 2 comma negative 4 close paren is a solution to Equation B
answer CORRECTLY
The solution to the system of equations is (5,8) - This statement is false. To find the solution to the system of equations, we need to solve for x and y. By doing so, we find that the solution is (4, 11), not (5,8).
(2,−4) is a solution to neither Equation - This statement is true. By substituting x = 2 and y = -4 into both equations, we find that neither equation is satisfied.
The y-intercept of Equation B is (0,12) - This statement is true. To find the y-intercept of Equation B, we set x = 0 and solve for y. Doing so, we get y = -12. Therefore, the y-intercept is (0, -12).
The slope of Equation A is m = −3 - This statement is false. To find the slope of Equation A, we can rearrange it into slope-intercept form (y = mx + b). By doing so, we get y = -3x + 23. Therefore, the slope of Equation A is -3, not -3.
(2,−4) is a solution to Equation B - This statement is false. By substituting x = 2 and y = -4 into Equation B, we find that the equation is not satisfied.