Equation A: 3x + y = 23
Equation B: 4x - y = 12
what are the system of equations to determine which of the following statements are true. Select all that apply.
O the y-intercept of equation b is (0,12)
O (2,-4) is a solution to equation b
O (2,-4) is a solution to neither equation
O The slope of equation A is m=-3
To determine which statements are true, we can analyze the given equations:
Equation A: 3x + y = 23
Equation B: 4x - y = 12
1. The y-intercept of equation B is (0,12):
To find the y-intercept of an equation, we set x = 0 and solve for y. In equation B, when x = 0, we have:
4(0) - y = 12
- y = 12
y = -12
So, the y-intercept of equation B is (0, -12), not (0, 12). Therefore, the statement "The y-intercept of equation B is (0, 12)" is false.
2. (2,-4) is a solution to equation B:
To check if (2,-4) is a solution to equation B, we substitute x = 2 and y = -4 into the equation:
4(2) - (-4) = 12
8 + 4 = 12
12 = 12
Since the equation is true when (x,y) = (2,-4), the statement "(2,-4) is a solution to equation B" is true.
3. (2,-4) is a solution to neither equation:
We've already determined that (2,-4) is a solution to equation B; therefore, this statement is false.
4. The slope of equation A is m = -3:
To find the slope of equation A, we rewrite it in slope-intercept form (y = mx + b):
3x + y = 23
y = -3x + 23
The slope (m) in this equation is -3. Therefore, the statement "The slope of equation A is m = -3" is true.
In conclusion, the following statements are true:
- (2,-4) is a solution to equation B
- The slope of equation A is m = -3