Step-by-step explanation:
We can solve this simultaneous equations by using the substitution method.
Equation 1:
[tex] - 2x + 3y = - 3[/tex]
Subtract 3y from both sides.
[tex] - 2x = - 3 - 3y[/tex]
Substitute that new equation into the second equation which is
[tex] - 2x - 5y = - 75[/tex]
to get
[tex] - 3 - 3y - 5y = - 75[/tex]
Simplify:
[tex] - 3 - 8y = - 75[/tex]
Add 3 to both sides:
[tex] - 8y = - 72[/tex]
Divide both sides by -8:
[tex]y = 9[/tex]
To solve for x, simply substitute y=9 into the first equation which is:
[tex] - 2x + 3y = - 3[/tex]
to get
[tex] - 2x + 3(9) = - 3[/tex]
[tex] - 2x + 27 = - 3[/tex]
Subtract 27 from both sides:
[tex] - 2x = - 30[/tex]
Hence,
[tex]x = 15[/tex]
and
[tex]y = 9[/tex]
