Question

Решить систему методом сложения:{4x-6y=2 2x-y=5

Answer 1

Answer:

$x=\frac{7}{2} =3.5\\\\y=2$

Step-by-step explanation:

The addition method (elimination method) allows us to combine two equations in such a way that the resulting equation has only one variable. Then we can use simple algebraic methods to solve that variable

Let:

$4x-6y=2\hspace{10}(1)\\\\and\\\\2x-y=5\hspace{15}(2)$

Let's multiply (2) by -2:

$-2*(2):\\\\2x(-2)-y(-2)=5(-2)\\\\-4x+2y=-10\hspace{12}(-2*(2))$

Now, add (1) and (-2*(2)):

$(1)+(-2*(2)):\\\\4x+(-4x)-6y+(2y)=2+(-10)\\\\-4y=-8$

Hence, solving for y:

$y=\frac{-8}{-4} =2$

Replacing y into (2):

$2x-(2)=5$

Solving for x:

$2x=5+2\\\\2x=7\\\\x=\frac{7}{2} =3.5$

Therefore:

$x=\frac{7}{2} =3.5\\\\y=2$