solve the system of linear equations by graphing.\ny = -\\frac{5}{2}x - 7\nx + 2y = 4\nwhat is the solution…

Explanation:

Step1: Rewrite second equation

Rewrite $x + 2y=4$ in slope - intercept form $y=mx + b$. $2y=-x + 4$, so $y=-\frac{1}{2}x+2$.

Step2: Analyze first equation

The first equation is $y =-\frac{5}{2}x-7$, with slope $m_1=-\frac{5}{2}$ and y - intercept $b_1=-7$.

Step3: Analyze second equation

The second equation $y =-\frac{1}{2}x + 2$ has slope $m_2=-\frac{1}{2}$ and y - intercept $b_2 = 2$.

Step4: Check each option

Substitute the x and y values of each option into both equations:

• For $(-4.5,4.25)$:
  • In $y=-\frac{5}{2}x-7$, $y=-\frac{5}{2}\times(-4.5)-7=\frac{22.5}{2}-7 = 11.25-7=4.25$.
  • In $x + 2y=4$, $-4.5+2\times4.25=-4.5 + 8.5 = 4$.
• For $(-1.7,-2.8)$:
  • In $y=-\frac{5}{2}x-7$, $y=-\frac{5}{2}\times(-1.7)-7=\frac{8.5}{2}-7=4.25 - 7=-2.75\neq-2.8$.
• For $(0,-7)$:
  • In $x + 2y=4$, $0+2\times(-7)=-14\neq4$.
• For $(3,0.5)$:
  • In $y=-\frac{5}{2}x-7$, $y=-\frac{5}{2}\times3-7=-\frac{15}{2}-7=-7.5 - 7=-14.5\neq0.5$.

Answer:

A. $(-4.5,4.25)$