A system of linear equations is shown on the graph.

Question

The graph shows two intersecting lines. One line passes through the points (negative 3, negative 4), (0, negative 2), and (3, 0). The other line passes through the points (negative 3, negative 4), (negative 1, 0), (0, 2), and (1, 4).

What is the solution to the system of equations? Type the coordinates in the boxes below.

Answer 1

The solution to the system of equations is the point where the two lines intersect. To find this point, we can set the equations of the two lines equal to each other and solve for the variables.

First, let's find the equation of the first line. Since it passes through the points (-3, -4), (0, -2), and (3, 0), we can use the point-slope form of a linear equation.

Using the point (-3, -4), we have:
y - y1 = m(x - x1)
y - (-4) = m(x - (-3))
y + 4 = m(x + 3)

Using the point (0, -2), we have:
y - y2 = m(x - x2)
y - (-2) = m(x - 0)
y + 2 = mx

Now, we can rewrite the equation with the slope (m) in terms of the two points (-3, -4) and (0, -2):
y + 4 = ((-2 - (-4))/(0 - (-3)))(x + 3)
y + 4 = (2/3)(x + 3)
y + 4 = (2/3)x + 2
y = (2/3)x - 2

Now, let's find the equation of the second line. Since it passes through the points (-3, -4), (-1, 0), (0, 2), and (1, 4), we can use the point-slope form of a linear equation.

Using the point (-3, -4), we have:
y - y1 = m(x - x1)
y - (-4) = m(x - (-3))
y + 4 = m(x + 3)

Using the point (-1, 0), we have:
y - y2 = m(x - x2)
y - 0 = m(x - (-1))
y = mx + m

Using the point (0, 2), we have:
y - y3 = m(x - x3)
y - 2 = m(x - 0)
y - 2 = mx

Using the point (1, 4), we have:
y - y4 = m(x - x4)
y - 4 = m(x - 1)
y - 4 = mx - m

Now, we can rewrite the equation with the slope (m) in terms of the four points (-3, -4), (-1, 0), (0, 2), and (1, 4):
y + 4 = ((0 - (-4))/(-1 - (-3)))(x + 3)
y + 4 = (4/2)(x + 3)
y + 4 = 2(x + 3)
y + 4 = 2x + 6
y = 2x + 2

Now that we have the equations of the two lines, we can set them equal to each other:
(2/3)x - 2 = 2x + 2

To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction:
3*((2/3)x - 2) = 3*(2x + 2)
2x - 6 = 6x + 6

Next, we can subtract 2x from both sides of the equation to isolate the variable x:
2x - 6 - 2x = 6x + 6 - 2x
-6 = 4x + 6

Now, we can subtract 6 from both sides of the equation to isolate the variable x:
-6 - 6 = 4x + 6 - 6
-12 = 4x

Finally, we can divide both sides of the equation by 4 to solve for x:
(-12)/4 = (4x)/4
-3 = x

Now that we have the value of x, we can substitute it back into one of the equations to solve for y. Let's use the equation y = 2x + 2:
y = 2*(-3) + 2
y = -6 + 2
y = -4

Therefore, the solution to the system of equations is (-3, -4).

So the solution is (-3, -4) in the appropriate boxes.

Answer 2

A system of equations is given below.

{x + 3y = 15
{3x + 2y = 10
What is the value of y for the solution to the system? Type your response in the box below.

y =

Answer 3

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