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![Find the solution of the system of equations.
{:[4x-8y=16],[8x-9y=39]:}](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/dm/Grade-8/Systems%20of%20Equations/Elimination%20%28Level%202%29/Q-33.png)
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Q. Find the solution of the system of equations.
- Write Equations: Write down the system of equations to be solved.We have the following system of equations:\begin{cases}4x-8y=16\8x-9y=39\end{cases}
- Choose Method: Decide on a method to solve the system of equations. We can use either substitution or elimination. In this case, we will use the elimination method because the coefficients of in both equations are multiples of each other, which makes it easier to eliminate one variable.
- Multiply First Equation: Multiply the first equation by to make the coefficients of in both equations the same.This gives us:
- New System After Multiplication: Write down the new system of equations after the multiplication.Now we have:\({:\begin{align*}[8x-16y&=32],\[8x-9y&=39]:\end{align*}\)
- Subtract Equations: Subtract the second equation from the first to eliminate \(x\).\((8x - 16y) - (8x - 9y) = 32 - 39\)This simplifies to:\(-16y + 9y = -7\)
- Solve for y: Solve for y.\(\newline\)\(-16y + 9y = -7\)\(\newline\)\(-7y = -7\)\(\newline\)\(y = -7 / -7\)\(\newline\)\(y = 1\)
- Substitute and Solve for \(x\): Substitute the value of \(y\) back into one of the original equations to solve for \(x\). We can use the first original equation: \(4x - 8y = 16\) Substitute \(y = 1\): \(4x - 8(1) = 16\) \(4x - 8 = 16\)
- Substitute and Solve for \(x\): Substitute the value of \(y\) back into one of the original equations to solve for \(x\). We can use the first original equation: \(4x - 8y = 16\) Substitute \(y = 1\): \(4x - 8(1) = 16\) \(4x - 8 = 16\) Solve for \(x\). \(4x - 8 = 16\) \(4x = 16 + 8\) \(y\)\(0\) \(y\)\(1\) \(y\)\(2\)
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