Answer:
The solution of this system of linear equations is [tex](x,y) = (-3,-2)[/tex].
Step-by-step explanation:
Let be the following system of linear equations:
[tex]2\cdot x - 7\cdot y = 8[/tex] (1)
[tex]-3\cdot x + 2\cdot y = 5[/tex] (2)
From (1) we clear [tex]y[/tex]:
[tex]2\cdot x -8 = 7\cdot y[/tex]
[tex]y = \frac{2\cdot x - 8}{7}[/tex]
And we apply this variable in (2):
[tex]-3\cdot x+2\cdot \left(\frac{2\cdot x -8}{7} \right)= 5[/tex]
[tex]-3\cdot x +\frac{4}{7} \cdot x -\frac{16}{7} = 5[/tex]
[tex]-\frac{17}{7}\cdot x = \frac{51}{7}[/tex]
[tex]x = -\frac{51}{17}[/tex]
[tex]x = -3[/tex]
And the value of [tex]y[/tex] is:
[tex]y = \frac{2\cdot (-3)-8}{7}[/tex]
[tex]y = -\frac{14}{7}[/tex]
[tex]y = -2[/tex]
The solution of this system of linear equations is [tex](x,y) = (-3,-2)[/tex].
