Final answer:
To solve the simultaneous linear equations 3x + 2y = 26 and 4x + y = 28, the elimination method is used, resulting in the solution x = 6 and y = 4.
Step-by-step explanation:
To solve the simultaneous linear equations 3x + 2y = 26 and 4x + y = 28, we can use the method of substitution or elimination. Let's use the elimination method for this example:
- Multiply the second equation by 2 to make the coefficients of y the same: 8x + 2y = 56.
- Subtract the first equation from the new equation obtained in step 1 to eliminate y: (8x + 2y) - (3x + 2y) = 56 - 26, which simplifies to 5x = 30.
- Divide both sides by 5 to find the value of x: x = 6.
- Substitute x back into either original equation to find y: Using the second original equation 4x + y = 28, substitute x: 4(6) + y = 28, which simplifies to 24 + y = 28.
- Subtract 24 from both sides to solve for y: y = 4.
Therefore, the solution to the system of equations is x = 6 and y = 4.