Solve the system of equtions.

Question

I tried to do it twice and i already failed it twice. i really need a good grade to pass trig. but these two questions are the ones stopping me. please show work. i really apricate all your help

1. x+y=5, y=7-x

2. 3x-y=2 16x-5y=11

Answer 1

Substitution method :

1).

The system of equations are x + y = 5 and y = 7 - x.

Substitute y = 7 - x in x + y = 5  and solve for x.

x + ( 7 - x ) = 5

7 = 5.

The above statement is false, so, there is no solutions exists to the given system.

2).

The system of equations are

3x - y = 2        → ( 1 )

16x - 5y = 11   → ( 2 )

From eq ( 1 ) y = 3x - 2.

Substitute y = 3x - 2 in 16x - 5y = 11 and solve for x.

16x - 5( 3x - 2 ) = 11

16x - 15x + 10 = 11

x = 11 - 10 = 1.

Substitute the value x = 1 in y = 3x - 2, and solve for y.

y = 3(1) - 2

y = 1.

The solution of the given system is x = 1 and y = 1.

Comments

Yes, anwers are correct.

1. write the equations in standard form x+ y = 5 x + y = 7 Observe the line equations, they are parallel. They will not intersect each other. No solutions.