Answer:
[tex]x = -7 [/tex]
[tex]y = - 12[/tex]
Step-by-step explanation:
The given system is:
4x-3y=8
5x-2y=-11
We make x the subject in the top equation to get:
[tex]x = \frac{3}{4}y + 2[/tex]
Plug this expression for x in the bottom equation to get
[tex]5( \frac{3}{4}y + 2) - 2y= - 11[/tex]
We expand to obtain
[tex] \frac{15}{4} y + 10 - 2y = - 11[/tex]
Multiply through by 4
[tex]15y + 40 - 8y = - 44[/tex]
Group similar terms
[tex]15y - 8y = - 44 - 40[/tex]
[tex]7y = - 84[/tex]
[tex]y = - \frac{84}{7} =-12 [/tex]
This means
[tex]x = -12\times \frac{3}{4} + 2[/tex]
[tex]x = - 7[/tex]
