Part 1)
we have
\(3x-6y=3\) ------> equation A
\(7x-5y=-11\) ------> equation B
Multiply by \(-7\) the equation A
\(-7(3x-6y)=-7*3\)
\(-21x+42y=-21\) ------> equation C
Multiply by \(3\) the equation B
\(3*(7x-5y)=-11*3\)
\(21x-15y=-33\) -------> equation D
Adds equation C and equation D
\(-21x+42y=-21 \\21x-15y=-33\\---------- \\ 42y-15y=-21-33\\27y=-54 \\ y=-2\)
therefore
the answer Part 1) is the option A
\(y=-2\)
Part 2)
we have
\(3x+y=6\)
\(y=-3x+6\) ------> equation A
\(6x+2y=8\)
Simplify Divide by \(2\) both sides
\(3x+y=4\)
\(y=-3x+4\) ------> equation B
the lines A and B are parallel lines, because the slope m is equal
so
The system has no solution
therefore
the answer Part 2) is the option D
There is no x value as there is no solution to the system.
Part 3)
we have
\(4x+2y=6\) ------> equation A
\(x-y=3\)
\(y=x-3\) ------> equation B
substitute equation B in equation A
\(4x+2[x-3]=6\)
\(6x-6=6\)
\(6x=12\)
\(x=2\)
therefore
the answer part 3) is the option D
\(x=2\)
Part 4)
Let
x---------> The number of one-step equations
y---------> The number of two-step equations
we know that
\(x+y=1,120\)
\(x=1,120-y\) -------> equation A
\(3x-2y=1,300\) ------> equation B
substitute equation A in equation B
\(3[1,120-y]-2y=1,300\)
\(3,360-5y=1,300\)
\(5y=3,360-1,300\)
\(5y=2,060\)
\(y=412\)
therefore
the answer part 4) is the option D
\(y=412\)
