Question

asked Oct 16, 2023 71.1k views

2 Answers

Ricardo Coelho · Answer 1 · 2023-10-21T18:24:53+0000

Step-by-step explanation:

Consider the following system of linear equations:

Equation 1:

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:

$y=\text{ -}(2)/(2)\text{ = - 1}$

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:

$x\text{ = -}(12)/(6)=\text{ -2}$

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

$y\text{ = -1}$

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