To solve the system of equations:

\[ 
3x_1 + 5x_2 = 45 
\]

\[ 
8x_1 - 9x_2 = 56 
\]

we can use the method of substitution or elimination. Here, I'll use the elimination method:

1. Multiply the first equation by 8 and the second equation by 3 to align the coefficients of \( x_1 \):

\[ 
8(3x_1 + 5x_2) = 8(45) \\
24x_1 + 40x_2 = 360 
\]

\[ 
3(8x_1 - 9x_2) = 3(56) \\
24x_1 - 27x_2 = 168 
\]

2. Subtract the second equation from the first:

\[ 
(24x_1 + 40x_2) - (24x_1 - 27x_2) = 360 - 168 \\
24x_1 + 40x_2 - 24x_1 + 27x_2 = 192 \\
67x_2 = 192 \\


Learn how to solve the system of linear equations 3x1 + 5x2 = 45 and 8x1 - 9x2 = 56 using the elimination method. This problem involves basic algebraic concepts and is suitable for high school students.

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