Solve the system of equation 5x+3y=55 and 4x-y=10

Eliminate y's

multiply 2nd equation by 3 and add to first

5x+3y=55

12x-3y=30 +

17x+0y=85

17x=85

divide both sides by 17

x=5

sub back

4x-y=10

4 (5) - y=10

20-y=10

-y=-10

y=10

x=5

y=10

(5,10)

or you could subsitution with y=4x-10

(5,10)

Problem:

Solve 5x+3y=55; 4x-y=10

Steps:

I will try to solve your system of equations.

4x-y=10; 5x+3y=55

Step: Solve 4x-y=10 for y:

4x-y+-4x=10+-4x (Add - 4x to both sides)

-y=-4x+10

-y

-1

=

-4x+10

-1

(Divide both sides by - 1)

y=4x-10

Step: Substitute (4x-10) for y in 5x+3y=55:

5x+3y=55

5x+3 (4x-10) = 55

17x-30=55 (Simplify both sides of the equation)

17x-30+30=55+30 (Add 30 to both sides)

17x=85

17x

17

=

85

17

(Divide both sides by 17)

x=5

Step: Substitute (5) for x in y=4x-10:

y=4x-10

y = (4) (5) - 10

y=10 (Simplify both sides of the equation)

Answer:

y=10 and x=5