Question

For each ordered pair determine whether it is a solution to the system of equations 2x-7y=8 -3x+2y=5

Answer 1

Answer:

The solution of this system of linear equations is $(x,y) = (-3,-2)$.

Step-by-step explanation:

Let be the following system of linear equations:

$2\cdot x - 7\cdot y = 8$ (1)

$-3\cdot x + 2\cdot y = 5$ (2)

From (1) we clear $y$:

$2\cdot x -8 = 7\cdot y$

$y = \frac{2\cdot x - 8}{7}$

And we apply this variable in (2):

$-3\cdot x+2\cdot \left(\frac{2\cdot x -8}{7} \right)= 5$

$-3\cdot x +\frac{4}{7} \cdot x -\frac{16}{7} = 5$

$-\frac{17}{7}\cdot x = \frac{51}{7}$

$x = -\frac{51}{17}$

$x = -3$

And the value of $y$ is:

$y = \frac{2\cdot (-3)-8}{7}$

$y = -\frac{14}{7}$

$y = -2$

The solution of this system of linear equations is $(x,y) = (-3,-2)$.