Marking !
the graph shows two lines, a and b.

based on the graph, which statement is correct about the solution to the system of equations for lines a and b?

(4, 4) is the solution to line a but not to line b.
(4, 4) is the solution to both lines a and b.
(5, 1) is the solution to line b but not to line a.
(0, 2) is the solution to both lines a and b.

(4, 4) is the solution to both lines A and B.

Step-by-step explanation:

The solution to a system of equations is the point at which the two lines intersect. Lines A and B intersect at point (4,4). This means (4,4) is the point which makes both equations true for the same values. The correct answer is     "(4, 4) is the solution to both lines A and B."

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3