Solve linear system using..multiplication and addition?

Question

x+3y=3 and 2g-3h=0

x+6y=3 3g-2h=5

Answer 1

I trust that you intend these as two problems.

Problem 1.

x + 3y = 3 :: {1}

x + 6y = 3 :: {2}

–x – 3y = –3 :: {3} = {1} X –1

3y = 0. :: {4} = {2} + {3}

–3y = 0. :: {5} = {4} X –1

x = 3. :: {6} = {1} + {5}

y = 0. :: {7} = ⅓ X {4}

Hence, solution is x = 3, y = 0.

Check: substitute these values into the original equations.

3 + 3(0) = 3.

3 + 6(0) = 3.

These check, so we must be doing something right.

Note, line numbers are shown in curly brackets { }.

Problem 2.

2g - 3h = 0 :: {1}

3g - 2h = 5 :: {2}

6g – 9h = 0 :: {3} = {1} X 3

–6g + 4h = –10 :: {4} = {2} X –2

–5h = –10 :: {5} = {3} + {4}

h = 2 :: {6} = {5} X – 1/5

2h = 4 :: {7} = {6} X 2

3g = 9 :: {8} = {2} + {7}

g = 3 :: {9} = {8} x ⅓

Hence, solution is g = 3, h = 2.

Again, we check by substituting these values into the original equations.

2(3) – 3(2) = 6 – 6 = 0.

3(3) – 2(2) = 9 – 4 = 5.

These answers appear to check, also.

I hope that these answers will be of help.