Question

Solve the following system of equations:-3x + 2y = 46x-2y= - 10X = ?Y = ?

Answer 1

Explanation:

Consider the following system of linear equations:

Equation 1:

$-3x+2y=4$

Equation 2:

$6x\text{ - 2y = -10}$

Adding 2 times equation 1 to equation 2, we get:

$(6x\text{ - 2y \rparen+2\lparen-3x +2y\rparen= -10 + 2\lparen4\rparen}$

this is equivalent to:

$6x\text{ -2y -6x +4y = -10 +8}$

this is equivalent to:

$\text{ - 2y + 4y = -2}$

this is equivalent to:

$2y=\text{ - 2}$

solving for y, we obtain:

$y=\text{ -}\frac{2}{2}\text{ = - 1}$

now, replacing this value in equation 2, we get:

$6x\text{ - 2\lparen -1\rparen = -10}$

this is equivalent to:

$6x+2=\text{ -10}$

solving for 6x, we get:

$6x\text{ = -10 -2 = -12}$

solving for x, we obtain:

$x\text{ = -}\frac{12}{6}=\text{ -2}$

we can conclude that the correct answer is:

Answer:

The solution of the given system of equations is:

$(x,\text{ }y)=\text{ \lparen-2, -1\rparen}$

that is:

$x\text{ = -2}$

and

$y\text{ = -1}$