Question

Solve the system 3x+2y=10 and y=2x-2. The solution is?

Answer 1

x = 2

y = 2

Explanation:

Solving system of linear equations by substitution method:

3x + 2y = 10 ----------------(I)

y = 2x - 2 ---------------(II)

Substitute y =2x -2 in equation (I)

3x + 2*(2x - 2) = 10

3x + 2*2x - 2*2 = 10

3x + 4x - 4 = 10

Add like terms,

7x - 4 = 10

Add 4 to both sides,

7x = 10 + 4

7x = 14

Divide both sides by 7

x = 14 ÷ 7

`\sf \boxed{x = 2}`

Substitute x = 2 in equation (I)

y = 2*2 - 2

= 4 - 2

y = 2

The solution: (2,2)

Answer 2

3x+2y=10 ------------------------------------(1)

y=2x-2.

Re-arrange the above

- 2x + y= -2 --------------------------------------(2)

We will solve by elimination;

We are going to eliminate y, to do that make the coefficient of y in the first and second equation the same.

This can be done by multiplying equation (1) by 1 and then multiply equation (2) by 2

That is;

3x + 2y = 10 ----------------------------------(3)

-4x + 2y = -4 --------------------------------------(4)

subtract equation (4) from equation (3)

7x= 14

divide both-side of the equation by 7

x=2

substitute x=2 into equation(2)

- 2x + y= -2

-2(2) + Y = -2

-4 + y = -2

add 4 to both-side of the equation

y = -2 + 4

y = 2

The solution is;

(2, 2)