Solve the following system of linear equations in the two unknowns 𝑥 and 𝑦 in terms of the constants 𝑎 and 𝑏.

Question

Solve the following system of linear equations in the two unknowns x and y in terms of the constants a and b.

4x+3y=a

5x+4y=b

x=

y=

Answer 1

4x+3y=a (1)

5x+4y=b (2)

multiply (1) by 5 and multiply (2) by 4

20x+15y=5a (3)

20x+16y=4b (4)

Eliminate x: (4)-(3)

y=4b-5a (5)

Substitue (5) into (1) to get x:

4x+3(4b-5a)=a

4x+12b-15a=a

4x=16a-12b

x=4a-3b

Therefore, x=4a-3b, y=4b-5a