Maths · Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
Solve for and by using method of substitution:
Solve for \( x \) and \( y \) by using method of substitution: \( \mathbf{0 . 2 x + 0 . 3 y}=\mathbf{1 . 3 ; 0 . 4 x + 0 . 5 y}=\mathbf{2 . 3} \)
- A. -2,-3
- B. 2,-3
- C. 2,3
- D. -2,3
Step-by-step solution
Multiply both equations by 10 to eliminate decimals: 2x + 3y = 13 and 4x + 5y = 23. Solve first for x: x = (13 - 3y)/2. Substitute into second: 2(13 - 3y) + 5y = 23 → 26 - 6y + 5y = 23 → 26 - y = 23 → y = 3. Then x = (13 - 9)/2 = 2. So the solution is (2,3).
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