Question

Solve for x and y
x+3y=3
3x+5y=5

Answer 1

x=3-3y------eq_i

3x=5-5y

x=5-5y--------eq_ii

3

equating eq i and ii

x=x

3-3y=5-5y

3

3(3-3y)=5-5y

9-9y=5-5y

-9y+5y=5-9

-4y= -4

y=1

now, subsituting the value of y in eq i

x=3-3y

x=3-3×1

x=3-3

x=0

Answer 2

x = 0, y = 1

Explanation:

This is a system of simultaneous equations in two variables

One method of solving is to get the coefficients of one of the variables same, add or subtract to eliminate that variable and solve for the other variable.

We have

x + 3y = 3 ...............[1]
3x +5y = 5................[2]

If we multiply Equation [1] by 3 we can get the x coefficients the same

[1] x 3 :

3x + 9y = 9..............[3]

Subtract equation [2] from equation [3]

[3] - [2]

(3x + 9y) - (3x + 5y) = 9-5

3x - 3x + 9y - 5y = 4

4y = 4

y = 1

Substitute for y = 1 in equation [1] to get

x + 3(1) = 3

x + 3 = 3

x = 0

So answer is

x = 0, y = 1