Solve using elimination. –8x − 3y = 11 –8x + 4y = 4 (_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by adding the two equations together because the coefficients of x are the same but with opposite signs. –8x − 3y = 11 –8x + 4y = 4Add Equations: Now, we add the two equations together to eliminate the x variable. (–8x − 3y) + (–8x + 4y) = 11 + 4 This simplifies to: –8x + 8x − 3y + 4y = 15Eliminate x: Simplifying the equation, we get: 0x + y = 15 Which means: y = 15Substitute y: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. We'll use the first equation: –8x − 3y = 11 Substituting y = 15, we get: –8x − 3(15) = 11Solve for x: Solving for x, we have: –8x − 45 = 11 Adding 45 to both sides gives us: –8x = 11 + 45 –8x = 56Find x Value: Now, we divide both sides by -8 to find the value of x: x = 56 / -8 x = -7Final Solution: We have found the values of x and y: x = -7, y = 15 So the solution to the system of equations is (-7, 15).

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Solve using elimination. $\newline$ $-8x - 3y = 11$ $\newline$ $-8x + 4y = 4$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-8x - 3y = 11

\newline

-8x + 4y = 4

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by adding the two equations together because the coefficients of $x$ are the same but with opposite signs. $-8x - 3y = 11$ $-8x + 4y = 4$
Add Equations: Now, we add the two equations together to eliminate the $x$ variable. $\newline$ $(-8x - 3y) + (-8x + 4y) = 11 + 4$ $\newline$ This simplifies to: $\newline$ $-8x + 8x - 3y + 4y = 15$
Eliminate x: Simplifying the equation, we get: $\newline$ $0x + y = 15$ $\newline$ Which means: $\newline$ $y = 15$
Substitute $y$ : Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . We'll use the first equation: $\newline$ $–8x − 3y = 11$ $\newline$ Substituting $y = 15$ , we get: $\newline$ $–8x − 3(15) = 11$
Solve for x: Solving for x, we have: $\newline$ $-8x - 45 = 11$ $\newline$ Adding $45$ to both sides gives us: $\newline$ $-8x = 11 + 45$ $\newline$ $-8x = 56$
Find x Value: Now, we divide both sides by $-8$ to find the value of $x$ :
$x = \frac{56}{-8}$
$x = -7$
Final Solution: We have found the values of $x$ and $y$ : $x = -7$ , $y = 15$ So the solution to the system of equations is $(-7, 15)$ .