Question

If 5x + y = 20 and 10x - 2y = 50 are two linear equations in two variables. Find the value of x and y.

x = 1, y = 1
x = 2, y = 1/2
x = 9/2, y = -5/2
x = 1, y = 5/2

Answer 1

x = 9/2, y = -5/2

Explanation:

5x + y = 20

10x - 2y = 50

There's multiple ways to do this, but I will solve using substitution.

Isolate variable y on the first equation.

5x + y = 20

y = 20 - 5x

Substitute the value of y for 20 - 5x in the second equation.

10x - 2(20 - 5x) = 50

Use distributive property:

10x - 40 + 10x = 50

Combine like terms:

20x - 40 = 50

20x = 90

x = 90/20

x = 9/2

Substitute x for 9/2 and solve for y:

y = 20 - 5(9/2)

y = 20 - 45/2

y = 40/2 - 45/2

y = -5/2

Answer 2

x =9/2, y = -5/2

Explanation:

5(9/2) + -(5/2)= 20

45/2 + -5/2 = 20

40/2 = 20

10(9/2) - 2(-5/2) = 50

90/2 + 10/2 = 50

45 + 5 = 50