To solve the system of linear equations given by 6x + 7y = 59 and 4x + 5y = 41, we can use the method of substitution or elimination. Here, we’ll use the elimination method.
First, we’ll align the equations for clarity:
1) 6x + 7y = 59
2) 4x + 5y = 41
We can multiply the second equation by 1.5 to make the coefficient of x in both equations similar:
3) 1.5 * (4x + 5y) = 1.5 * 41
Which simplifies to:
3) 6x + 7.5y = 61.5
Now we have:
- 6x + 7y = 59
- 6x + 7.5y = 61.5
Next, we subtract the first equation from the modified second equation:
(6x + 7.5y) – (6x + 7y) = 61.5 – 59
This results in:
0.5y = 2.5
Solving for y, we divide both sides by 0.5:
y = 2.5 / 0.5 = 5
Now that we have y, we substitute this value back into one of the original equations to find x. We can use the first equation:
6x + 7(5) = 59
This simplifies to:
6x + 35 = 59
Subtracting 35 from both sides gives us:
6x = 24
Dividing both sides by 6 yields:
x = 4
Thus, the solution to the system of equations is:
x = 4 and y = 5.
In conclusion, the values of x and y satisfy both equations, confirming they are the correct solution.