Solve the system of equations. 8x - 4y = -8 x + 3y = 20 (____, ____)

Simplify equation: Step 1: Simplify the first equation by dividing all terms by 4. 8x - 4y = -8 becomes 2x - y = -2. Solve for y: Step 2: Solve for y in terms of x from the simplified equation. y = 2x + 2. Substitute y into second equation: Step 3: Substitute y = 2x + 2 into the second equation x + 3y = 20. x + 3(2x + 2) = 20, x + 6x + 6 = 20, 7x + 6 = 20. Solve for x: Step 4: Solve for x. 7x = 20 - 6, 7x = 14, x = 2. Substitute x back into y: Step 5: Substitute x = 2 back into y = 2x + 2 to find y. y = 2(2) + 2, y = 4 + 2, y = 6.

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Solve the system of equations. $\newline$ $8x - 4y = -8$ $\newline$ $x + 3y = 20$ $\newline$ (, )

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Algebra 2

Solve a system of equations in three variables using elimination

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Q. Solve the system of equations.

\newline

8x - 4y = -8

\newline

x + 3y = 20

\newline

(____, ____)

Simplify equation: Step $1$ : Simplify the first equation by dividing all terms by $4$ . $8x - 4y = -8$ becomes $2x - y = -2$ .
Solve for $y$ : Step $2$ : Solve for $y$ in terms of $x$ from the simplified equation. $y = 2x + 2.$
Substitute $y$ into second equation: Step $3$ : Substitute $y = 2x + 2$ into the second equation $x + 3y = 20$ .
$x + 3(2x + 2) = 20$ ,
$x + 6x + 6 = 20$ ,
$7x + 6 = 20$ .
Solve for x: Step $4$ : Solve for x. $\newline$ $7x = 20 - 6$ , $\newline$ $7x = 14$ , $\newline$ $x = 2$ .
Substitute $x$ back into $y$ : Step $5$ : Substitute $x = 2$ back into $y = 2x + 2$ to find $y$ . $y = 2(2) + 2$ , $y = 4 + 2$ , $y = 6$ .