To solve the given system of linear equations step-by-step, follow these instructions:
1. Simplify the First Equation:
The first equation is:
[tex]\[
2x - 324 + 30 = 0
\][/tex]
Combine like terms:
[tex]\[
2x - 294 = 0
\][/tex]
Isolate the variable x:
[tex]\[
2x = 294
\][/tex]
Solve for x by dividing both sides by 2:
[tex]\[
x = \frac{294}{2}
\][/tex]
Consequently:
[tex]\[
x = 147
\][/tex]
2. Substitute [tex]\( x = 147 \)[/tex] into the Second Equation:
The second equation is:
[tex]\[
32x + 29y - 35 = 0
\][/tex]
Substitute [tex]\( x = 147 \)[/tex] into the equation:
[tex]\[
32(147) + 29y - 35 = 0
\][/tex]
Calculate [tex]\( 32 \times 147 \)[/tex]:
[tex]\[
32 \times 147 = 4704
\][/tex]
The equation then transforms into:
[tex]\[
4704 + 29y - 35 = 0
\][/tex]
Simplify the equation:
[tex]\[
4704 - 35 + 29y = 0
\][/tex]
[tex]\[
4669 + 29y = 0
\][/tex]
Isolate the variable y by subtracting 4669 from both sides:
[tex]\[
29y = -4669
\][/tex]
Solve for y by dividing both sides by 29:
[tex]\[
y = \frac{-4669}{29}
\][/tex]
Consequently:
[tex]\[
y = -161
\][/tex]
Thus, the solution to the system of linear equations is:
[tex]\[
x = 147, \quad y = -161
\][/tex]
