Question

y = -\frac{7}{4}x + \frac{5}{2}
y = \frac{3}{4}x - 3
which points are possible approximations for this system? select two options
\square (1.9, 2.5)
\square (2.2, -1.4)
\square (2.2, -1.35)

Explanation:

Step1: Find exact intersection

Set equations equal:
$$-\frac{7}{4}x + \frac{5}{2} = \frac{3}{4}x - 3$$
Multiply all terms by 4:
$$-7x + 10 = 3x - 12$$
Rearrange to solve for $x$:
$$-7x - 3x = -12 - 10$$
$$-10x = -22$$
$$x = \frac{22}{10} = 2.2$$

Step2: Calculate y-value

Substitute $x=2.2$ into $y=\frac{3}{4}x - 3$:
$$y = \frac{3}{4}(2.2) - 3 = 1.65 - 3 = -1.35$$

Step3: Match to options

Compare exact values $(2.2, -1.35)$ to given choices.

Answer:

B. (2.2, -1.4)
C. (2.2, -1.35)