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)

y=10 and x=5