what is the solution to the system of equations graphed below
y=2x-7
y=-x-1
To find the solution to the system of equations, we need to find the intersection point of the two lines. From the graph, we can see that the lines intersect at the point (-2, -3). Therefore, the solution to the system of equations is x = -2 and y = -3.
i have a (3,-2) b (0,-1) c (4,1) d (2,-3)
To find the solution to the system of equations using the given points, we can substitute the x and y values of each point into both equations and check if the equations hold true.
For point A (3, -2):
y = 2x - 7
-2 = 2(3) - 7
-2 = 6 - 7
-2 = -1 (not true)
This point does not satisfy the first equation.
y = -x - 1
-2 = -(3) - 1
-2 = -3 - 1
-2 = -4 (not true)
This point does not satisfy the second equation.
For point B (0, -1):
y = 2x - 7
-1 = 2(0) - 7
-1 = 0 - 7
-1 = -7 (not true)
This point does not satisfy the first equation.
y = -x - 1
-1 = -(0) - 1
-1 = 0 - 1
-1 = -1 (true)
This point satisfies the second equation.
For point C (4, 1):
y = 2x - 7
1 = 2(4) - 7
1 = 8 - 7
1 = 1 (true)
This point satisfies the first equation.
y = -x - 1
1 = -(4) - 1
1 = -4 - 1
1 = -5 (not true)
This point does not satisfy the second equation.
For point D (2, -3):
y = 2x - 7
-3 = 2(2) - 7
-3 = 4 - 7
-3 = -3 (true)
This point satisfies the first equation.
y = -x - 1
-3 = -(2) - 1
-3 = -2 - 1
-3 = -3 (true)
This point satisfies the second equation.
From the given points, only point D (2, -3) satisfies both equations. Therefore, the solution to the system of equations is x = 2 and y = -3.