Solve using elimination. $\newline$ $9x + 9y = 9$ $\newline$ $5x + 9y = -15$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

9x + 9y = 9

\newline

5x + 9y = -15

\newline

(_____, _____)

Write Equations: First, let's write down the system of equations we need to solve: $\newline$ $9x + 9y = 9$ $\newline$ $5x + 9y = -15$ $\newline$ We want to eliminate one of the variables by subtracting one equation from the other. Since the coefficients of $y$ are the same in both equations, we can subtract the second equation from the first to eliminate $y$ .
Subtract Equations: Perform the subtraction of the two equations: $\newline$ $(9x + 9y) - (5x + 9y) = 9 - (\text{–}15)$ $\newline$ This simplifies to: $\newline$ $9x - 5x + 9y - 9y = 9 + 15$
Combine Like Terms: Simplify the equation by combining like terms: $\newline$ $4x + 0y = 24$ $\newline$ This simplifies to: $\newline$ $4x = 24$
Solve for x: Now, solve for x by dividing both sides of the equation by $4$ : $\newline$ $\frac{4x}{4} = \frac{24}{4}$ $\newline$ $x = 6$
Substitute $x$ : With the value of $x$ found, we can substitute it back into one of the original equations to find the value of $y$ . Let's use the first equation: $\newline$ $9x + 9y = 9$ $\newline$ $9(6) + 9y = 9$
Solve for y: Substitute $x = 6$ into the equation and solve for y: $\newline$ $54 + 9y = 9$ $\newline$ $9y = 9 - 54$ $\newline$ $9y = -45$
Final Solution: Now, solve for $y$ by dividing both sides of the equation by $9$ : $\frac{9y}{9} = \frac{-45}{9}$ $y = -5$
Final Solution: Now, solve for $y$ by dividing both sides of the equation by $9$ : $\frac{9y}{9} = \frac{-45}{9}$ $y = -5$ We have found the values of $x$ and $y$ that solve the system of equations: $x = 6, y = -5$ These values are the solution to the system of equations.