Solve using elimination. x + 6y = –15 –2x + 6y = 12 (___,___)

System of equations: System of equations: x + 6y = -15 -2x + 6y = 12 We need to decide which variable to eliminate. Since the coefficients of y are the same in both equations, we will eliminate y.Eliminating y: System of equations: x + 6y = -15 -2x + 6y = 12 To eliminate y, we will subtract the second equation from the first.Subtracting equations: Subtract the equations to eliminate y: (x + 6y) - (-2x + 6y) = -15 - 12 x + 6y + 2x - 6y = -27 3x = -27 We have successfully eliminated y and found an equation with only x.Solving for x: Solve for x: 3x = -27 Divide both sides of the equation by 3 to isolate x: (3x) / 3 = -27 / 3 x = -9 We have found the value of x.Substituting x into first equation: Substitute x = -9 into the first equation x + 6y = -15 to solve for y: -9 + 6y = -15 Add 9 to both sides to isolate the term with y: -9 + 9 + 6y = -15 + 9 6y = -6 Divide both sides by 6 to solve for y: y = -6 / 6 y = -1 We have found the value of y.Finding the value of y: We have found the values of x and y: x = -9 y = -1 We write the solution as a coordinate point. Solution: (-9, -1)

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Solve using elimination. $\newline$ $x + 6y = -15$ $\newline$ $-2x + 6y = 12$ $\newline$ $(\_,\_)$

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Algebra 1

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

x + 6y = -15

\newline

-2x + 6y = 12

\newline

(\_,\_)

System of equations: System of equations: $\newline$ $x + 6y = -15$ $\newline$ $-2x + 6y = 12$ $\newline$ We need to decide which variable to eliminate. $\newline$ Since the coefficients of $y$ are the same in both equations, we will eliminate $y$ .
Eliminating y: System of equations: $\newline$ $x + 6y = -15$ $\newline$ $-2x + 6y = 12$ $\newline$ To eliminate y, we will subtract the second equation from the first.
Subtracting equations: Subtract the equations to eliminate $y$ :
$(x + 6y) - (-2x + 6y) = -15 - 12$
$x + 6y + 2x - 6y = -27$
$3x = -27$
We have successfully eliminated $y$ and found an equation with only $x$ .
Solving for x: Solve for x: $\newline$ $3x = -27$ $\newline$ Divide both sides of the equation by $3$ to isolate x: $\newline$ $\frac{3x}{3} = \frac{-27}{3}$ $\newline$ x = $-9$ $\newline$ We have found the value of $x$ .
Substituting $x$ into first equation: Substitute $x = -9$ into the first equation $x + 6y = -15$ to solve for $y$ :
$-9 + 6y = -15$
Add $9$ to both sides to isolate the term with $y$ :
$-9 + 9 + 6y = -15 + 9$
$6y = -6$
Divide both sides by $6$ to solve for $y$ :
$x = -9$ $1$
$x = -9$ $2$
We have found the value of $y$ .
Finding the value of y: We have found the values of x and y: $\newline$ x = $-9$ $\newline$ y = $-1$ $\newline$ We write the solution as a coordinate point. $\newline$ Solution: $(-9, -1)$