Question

Solve the system 2x-2y=10 4x-5y=17

Answer 1

Multiply 2x-2y=10 by 2,
4x-4y=20,
given:4x-5y=17
y=3
pluck it in
2x-6=10
move the 6 to the right
2x=16
divide
x=8
y=3

Answer 2

Equation 1)  2x - 2y = 10
Equation 2)  4x - 5y = 17

Multiply ALL of equation 1 by 2.

1)  2(2x - 2y = 10)

Simplify.

1)  4x - 4y = 20
2)  4x - 5y = 17

Subtract equations from one another.

y = 3

Plug in 3 for y in the first equation.

1)  2x - 2y = 10

2x - 2(3) = 10

Simplify.

2x - 6 = 10

Add 6 to both side.s

2x = 16

Divide both sides by 2.

x = 8

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Check your work by plugging in 8 for x, and 3 for y into the original equations.

2x - 2y = 10 & 4x - 5y = 17

1)  2x - 2y = 10

2(8) - 2(3) = 10

Simplify.

16 - 6 = 10

10 = 10 

2)  4x - 5y = 17

4(8) - 5(3) = 17

Simplify.

32 - 15 = 17

17 = 17

Therefore, x = 8, y = 3

~Hope I helped!~