Question

Section B.3 - Algebra - Simultaneous and Quadratic Equations Solve problems 1 and 2 using the comparison, elimination, or substitution method.

1) x +y =2 2x -3y =5

2 ) 3x - 5y=5 7x + y = 75

Answer 1

1)

x+y=2
2x-3y=5

Multiply the 1st row by 2

2x+2y=4

2x-3y=5

Subtract the 2nd row from the 1st row

5y=−1

Divide both sides by 5

y= -1/5

Substitute -1/5 for y in x+y=2 and then solve for x as

x+(-1/5) =2

x= 2 +1/5

x=11/5

Thus, solution is

x=11/5, y= -1/5

2)

Multiply the 2nd row by -5

3x-5y=5
-35x-5y=-375

Subtract the 2nd row from the 1st row

38x=380

Divide both sides by 38

x=380/38

x=10

Substitute 10 for x in 7x + y = 75 and then solve for y as

7(10) +y= 75

70+y=75

y=75-70

y=5

Thus, solution is

x=10, y=5