Write as a Vector Equality (x+5)/2-(y+5)/3=4 , (x+y)/2=1/3+(x-y)/3

Problem

{[(x+5)/2−(y+5)/3=4],[(x+y)/2=1/3+(x−y)/3])

Solution

1. Clear the fractions in the first equation by multiplying every term by the least common multiple, 6

6*((x+5)/2)−6*((y+5)/3)=6*(4)

3*(x+5)−2*(y+5)=24

3*x+15−2*y−10=24

3*x−2*y=19

2. Clear the fractions in the second equation by multiplying every term by the least common multiple, 6

6*((x+y)/2)=6*(1/3)+6*((x−y)/3)

3*(x+y)=2+2*(x−y)

3*x+3*y=2+2*x−2*y

x+5*y=2

3. Identify the coefficients of x and y from both simplified equations to form the vectors.

Equation 1: *3*x−2*y=19

Equation 2: *1*x+5*y=2

4. Express as a vector equality by grouping the x terms, y terms, and constants into column vectors.

x*([3],[1])+y*([−2],[5])=([19],[2])

Final Answer

x*([3],[1])+y*([−2],[5])=([19],[2])

Want more problems? Check here!