Question

Solve the system x+3y=22 2x-y=2

Answer 1

Answer:  The required solution is (x, y) = (4, 6).

Step-by-step explanation:  We are given to solve the following system of equations :

$x+3y=22~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (ii), we have

$2x-y=2\\\\\Rightarrow y=2x-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (i), we get

$x+3(2x-2)=22\\\\\Rightarrow x+6x-6=22\\\\\Rightarrow 7x=22+6\\\\\Rightarrow 7x=28\\\\\Rightarrow x=\dfrac{28}{7}\\\\\Rightarrow x=4.$

From equation (i), we get

$4+3y=22\\\\\Rightarrow 3y=22-4\\\\\Rightarrow 3y=18\\\\\Rightarrowy=\dfrac{18}{3}\\\\\Rightarrow y=6.$

Thus, the required solution is (x, y) = (4, 6).

Answer 2

It will equal (4,6) for x and y