Which graph represents the solution to the given system -2+5y=-10 and -3x+5y=-20
To find the solution to the system -2+5y=-10 and -3x+5y=-20, we can solve it using the method of substitution or elimination.
Let's use the elimination method:
Multiply both sides of the first equation by -1:
-1*(-2+5y) = -1*(-10)
2-5y = 10
Multiply both sides of the second equation by -2:
-2*(-3x+5y) = -2*(-20)
6x-10y = 40
Now we have the two equations:
2-5y = 10
6x-10y = 40
Rearrange the first equation to solve for y:
-5y = 10-2
-5y = 8
y = 8/(-5)
y = -8/5
Substitute this value of y into the second equation and solve for x:
6x-10(-8/5) = 40
6x + 16 = 40
6x = 40-16
6x = 24
x = 24/6
x = 4
Therefore, the solution to the system is x = 4 and y = -8/5.
Now let's analyze the options given for the graph:
Option a: This graph intersects the x-axis at 4 and the y-axis at -2, which does not match the solution x = 4 and y = -8/5. Therefore, this graph does not represent the solution to the given system.
Option b: This graph intersects the x-axis at 4 and the y-axis at -8/5, which matches the solution x = 4 and y = -8/5. Therefore, this graph represents the solution to the given system.
Option c: This graph intersects the x-axis at 4 and the y-axis at -7, which does not match the solution x = 4 and y = -8/5. Therefore, this graph does not represent the solution to the given system.
Therefore, the correct graph that represents the solution to the given system is option b.