Question

your answer.
use elimination to determine the y - valu
$-2x + y = 6$
$5x + 2y = 3$
$y = \square$

Explanation:

Step1: Multiply first equation by 2

To eliminate \( y \), we multiply the first equation \(-2x + y = 6\) by 2. This gives \( 2(-2x + y)=2\times6 \), which simplifies to \(-4x + 2y = 12\).

Step2: Subtract the new equation from the second equation

The second equation is \( 5x + 2y = 3 \). Subtract \(-4x + 2y = 12\) from it: \((5x + 2y)-(-4x + 2y)=3 - 12\). Simplifying the left side: \(5x + 2y + 4x - 2y = 9x\), and the right side: \( -9 \). So \( 9x=-9 \), which gives \( x = - 1 \).

Step3: Substitute x into the first equation to find y

Substitute \( x=-1 \) into \(-2x + y = 6\). We get \(-2(-1)+y = 6\), which is \( 2 + y = 6 \). Subtract 2 from both sides: \( y=6 - 2=4 \).

Answer:

\( 4 \)