{:[2x-y=7],[2x+7y=31]:} 524 Chapter 9

Write Equations: First, let's write down the system of equations: {:[2x-y=7],[2x+7y=31]:}Elimination Method: We can use substitution or elimination to solve this system. I'll go with elimination. Let's multiply the first equation by 7 to get the y terms to cancel out. 7(2x - y) = 7(7) 14x - 7y = 49New System of Equations: Now we have a new system of equations: {:[14x-7y=49],[2x+7y=31]:}Add Equations: Next, we add the two equations together to eliminate y: (14x - 7y) + (2x + 7y) = 49 + 31 16x = 80Solve for x: Now, we divide both sides by 16 to solve for x: 16x / 16 = 80 / 16 x = 5Substitute x: We substitute x = 5 back into one of the original equations to solve for y. I'll use the first one: 2(5) - y = 7 10 - y = 7Solve for y: Subtract 10 from both sides to solve for y: -y = 7 - 10 -y = -3Final Result: Finally, we multiply both sides by -1 to get y: y = 3

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$\begin{array}{l} 2 x-y=7 \\ 2 x+7 y=31 \end{array}$

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Grade 8

Solve a system of equations using any method

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\begin{array}{l} 2 x-y=7 \\ 2 x+7 y=31 \end{array}

Write Equations: First, let's write down the system of equations: $\newline$ {\begin{cases}2x-y=7\2x+7y=31\end{cases}}
Elimination Method: We can use substitution or elimination to solve this system. I'll go with elimination. Let's multiply the first equation by $7$ to get the $y$ terms to cancel out. $\newline$ $7(2x - y) = 7(7)$ $\newline$ $14x - 7y = 49$
New System of Equations: Now we have a new system of equations: $\begin{cases} 14x-7y=49 \ 2x+7y=31 \end{cases}$
Add Equations: Next, we add the two equations together to eliminate $y$ : $(14x - 7y) + (2x + 7y) = 49 + 31$ $16x = 80$
Solve for x: Now, we divide both sides by $16$ to solve for x: $\newline$ $\frac{16x}{16} = \frac{80}{16}$ $\newline$ $x = 5$
Substitute $x$ : We substitute $x = 5$ back into one of the original equations to solve for $y$ . I'll use the first one: $\newline$ $2(5) - y = 7$ $\newline$ $10 - y = 7$
Solve for y: Subtract $10$ from both sides to solve for y: $\newline$ $-y = 7 - 10$ $\newline$ $-y = -3$
Final Result: Finally, we multiply both sides by $-1$ to get $y$ : $y = 3$