Question

For the simultaneous linear equations:

X + y = 4.15
y - x = 0.25

Can you please provide the steps to find the solution, which is x = 1.95 and y = 2.20?

Answer 1

see explanation

Step-by-step explanation:

given the simultaneous equations

x + y = 4.15 → (1)

- x + y = 0.25 → (2) [ with terms rearranged ]

adding the 2 equations term by term will eliminate x

(x - x) + (y + y) = 4.15 + 0.25

0 + 2y = 4.4

2y = 4.4 ( divide both sides by 2 )

y = 2.2

substitute y = 2.2 into (1) and solve for x

x + 2.2 = 4.15 ( subtract 2.2 from both sides )

x = 1.95

Then solution is x = 1.95 and y = 2.20

Answer 2

To solve the simultaneous linear equations x + y = 4.15 and y - x = 0.25, you can use the method of substitution. First, solve one equation for one variable in terms of the other, and then substitute that expression into the other equation. Solve for the remaining variable and substitute it back into one of the original equations to find the value of the other variable. In this case, x = 1.95 and y = 2.20.

Step-by-step explanation:

To solve the simultaneous linear equations x + y = 4.15 and y - x = 0.25, we can use the method of substitution. Here are the steps:

1. Choose one equation to solve for one variable in terms of the other.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of the variable found back into one of the original equations to find the value of the other variable.

For this specific problem, we can solve the second equation for y in terms of x: y = x + 0.25. Then, we substitute this expression into the first equation: x + (x + 0.25) = 4.15. Simplifying this equation gives us 2x + 0.25 = 4.15. Solving for x, we find x = 1.95. Substituting this value of x back into y = x + 0.25, we get y = 2.20.