Question

The graph shows a system of equations: Draw a line labeled y equal s x plus 4 by joining the ordered pairs negative 4, 0 and 1, 5. Draw a line labeled 3 times y equals minus 2 x plus 2 by joining the ordered pairs negative 2, 2 and 4, negative 2. What is the solution to the system of equations? (−2, 2) (2, 2) (2, −2) (−2, −2)

Answer 1

a: (-2,2) should be correct sorry if its wrong

Answer 2

(-2, 2)

Explanation:

In order to find the solution to the system of equations represented by the given lines, we need to find the point where the two lines intersect. This point is the solution to the system.

The two lines are:

1. y = x + 4 (Line passing through points A (-4,0) and B(1, 5))

2. 3y = -2x + 2 (Line passing through points C (-2, 2) and D(4, -2))

Simple Way:

By looking in the graph, the intersection point is (-2,2)

So, the answer is (-2,2)

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Another way

We can find the intersection point by equating the two equations:

y = x + 4

3y = -2x + 2

We can now substitute the value of y from the first equation into the second equation:

3(x + 4) = -2x + 2

Now, solve for x:

3x + 12 = -2x + 2

3x + 2x = 2 - 12

5x = -10

`\sf x =( -10)/(5)`

x = -2

Now, substitute the value of x back into either of the equations to find the y-coordinate:

y = -2 + 4

y = 2

So, the solution to the system of equations is the point (-2, 2).

Therefore, the correct answer is: (-2, 2)