Question

9
solve the system using elimination. show your work step by step.
(a) $x + y = 4$
$3x + 2y = 6$

Explanation:

Step1: Multiply first equation by 2

$2(x + y) = 2\times4$
$2x + 2y = 8$

Step2: Subtract second equation

Subtract $3x + 2y = 6$ from $2x + 2y = 8$:
$(2x + 2y) - (3x + 2y) = 8 - 6$
$2x + 2y - 3x - 2y = 2$
$-x = 2$
$x = -2$

Step3: Substitute x into first equation

Substitute $x=-2$ into $x + y = 4$:
$-2 + y = 4$
$y = 4 + 2$
$y = 6$

Answer:

$x=-2$, $y=6$