To determine if the system of equations is consistent and dependent, we need to find the x and y-intercepts of the equations.
For the first equation, 23x + 43y = 4, we can find the x-intercept by setting y = 0 and solving for x:
23x + 43(0) = 4
23x = 4
x = 4/23
For the y-intercept, we set x = 0 and solve for y:
23(0) + 43y = 4
43y = 4
y = 4/43
So the x-intercept is 4/23 and the y-intercept is 4/43 for the first equation.
Now, for the second equation, 2x + 4y = 12, we can find the x-intercept by setting y = 0 and solving for x:
2x + 4(0) = 12
2x = 12
x = 6
For the y-intercept, we set x = 0 and solve for y:
2(0) + 4y = 12
4y = 12
y = 3
So the x-intercept is 6 and the y-intercept is 3 for the second equation.
Since the two equations have different x and y-intercepts, the system is considered consistent and independent.
By finding the x - and y -intercepts, determine if the following system of equations is consistent and dependent. Explain your answer. 23x+43y=4 2x+4y=12 (1 point) Responses You cannot tell, because there are fractions in the first equation. You cannot tell, because there are fractions in the first equation. The system is not consistent and dependent, because the equations have the same x- and y-intercepts. The system is not consistent and dependent, because the equations have the same x - and y -intercepts. The system is consistent and dependent, because the equations have the same x- and y-intercepts. The system is consistent and dependent, because the equations have the same x - and y -intercepts. The system is consistent and dependent, because they have different x- and y-intercepts.
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