Answer:
(-1, -4)
Step-by-step explanation:
We have the following system of equations:
[tex]-4.5x-2y=12.5\\3.25x-y=0.75[/tex]
We can solve this using substitution.
First, from the second equation, let's subtract 3.25x from both sides. So:
[tex]-y=0.75-3.25x[/tex]
We can now substitute this into the first equation. Note that the first equation is the same as:
[tex]-4.5x+2(-y)=12.5[/tex]
Substitute in -y. This yields:
[tex]-4.5x+2(0.75-3.25x)=12.5[/tex]
Distribute:
[tex]-4.5x+1.5-6.5x=12.5[/tex]
Combine like terms:
[tex]-11x+1.5=12.5[/tex]
Subtract 1.5 from both sides:
[tex]-11x=11[/tex]
Divide both sides by -11. So, the value of x is:
[tex]x=-1[/tex]
To find y, we can use the equation we solved earlier:
[tex]-y=0.75-3.25x[/tex]
Substitute -1 for x:
[tex]-y=0.75-3.25(-1)[/tex]
Multiply:
[tex]-y=0.75+3.25[/tex]
Add:
[tex]-y=4[/tex]
Divide both sides by -1:
[tex]y=-4[/tex]
So, our solution is (-1, -4).
And we're done!
