We have been given a system of equations [tex]y=\frac{1}{2}x-4[/tex] and [tex]y=-2x-9[/tex]. We are asked to find the solution of our given system of equations.
To solve our system of equations, we will equate both equations as:
[tex]\frac{1}{2}x-4=-2x-9[/tex]
[tex]\frac{1}{2}x-4+4=-2x-9+4[/tex]
[tex]\frac{1}{2}x=-2x-5[/tex]
[tex]\frac{1}{2}x+2x=-2x+2x-5[/tex]
[tex]\frac{1}{2}x+\frac{4}{2}x=-5[/tex]
[tex]\frac{1+4}{2}x=-5[/tex]
[tex]\frac{5}{2}x=-5[/tex]
[tex]\frac{2}{5}\cdot \frac{5}{2}x=-5\cdot \frac{2}{5}[/tex]
[tex]x=-2[/tex]
Upon substituting [tex]x=-2[/tex] in equation [tex]y=-2x-9[/tex], we will get:
[tex]y=-2(-2)-9[/tex]
[tex]y=4-9[/tex]
[tex]y=-5[/tex]
Therefore, the solution of our given system of equations would be [tex](-2,-5)[/tex] and option A is the correct choice.
Answer:
is A: (–2, –5)
Step-by-step explanation:
i took the test and got it right
