Question

Solve the sysyem of equations 3x+y=3 x+y=2

Answer 1

Answer:

{x = 1/2 , y = 3/2

Step-by-step explanation:

Solve the following system:

{3 x + y = 3 | (equation 1)

{x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x + y = 3 | (equation 1)

{0 x+(2 y)/3 = 1 | (equation 2)

Multiply equation 2 by 3:

{3 x + y = 3 | (equation 1)

{0 x+2 y = 3 | (equation 2)

Divide equation 2 by 2:

{3 x + y = 3 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Subtract equation 2 from equation 1:

{3 x+0 y = 3/2 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 1/2 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Collect results:

Answer:  {x = 1/2 , y = 3/2

Answer 2

Answer:

$\large\boxed{x=\dfrac{1}{2}\ and\ y=1\dfrac{1}{2}\to\left(\dfrac{1}{2},\ 1\dfrac{1}{2}\right)}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}3x+y=3\\x+y=2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+y=3\\-x-y=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=1\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=\dfrac{1}{2}}\\\\\text{Put the value of x to the second equation:}\\\dfrac{1}{2}+y=2\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\boxed{y=1\dfrac{1}{2}}$