Question

solve the system of equations to identify the point of intersection and then identify which image correctly shows the equations graphed.

select one point of intersection and one coordinate plane below.

\\(8x + y = 10\\)
\\(3x + y = 5\\)

a. point of intersection = \\((-1, 2)\\)
b. point of intersection = \\((1, -2)\\)
c. point of intersection = \\((1, 2)\\)
d. point of intersection = \\((-1, -2)\\)

Explanation:

Solve the system of equations

Using the Linear Equations Solving knowledge point

$$
LATEXBLOCK0
$$

Subtract equation (2) from equation (1):

$$
LATEXBLOCK1
$$

Find the corresponding y-value

Using the Linear Equations Solving knowledge point
Substitute \(x = 1\) into equation (2):

$$
LATEXBLOCK2
$$

The point of intersection is \((1, 2)\).

Identify the correct graphs

Using the Graphing Linear Equations knowledge point
Convert both equations to slope-intercept form to identify their graphs:

• First line: \(y = -8x + 10\) (y-intercept is \(10\), slope is \(-8\))
• Second line: \(y = -3x + 5\) (y-intercept is \(5\), slope is \(-3\))

Both lines have negative slopes and intersect at the point \((1, 2)\).

Answer:

• a. Point of intersection = \((-1, 2)\)
• b. Point of intersection = \((1, -2)\)
• c. Point of intersection = \((1, 2)\) (Correct answer)
• d. Point of intersection = \((-1, -2)\)