Final answer:
The solution to the simultaneous equations 3y - x = 4 and 5y - 2x = 3 is x = 11 and y = 5. This is determined by expressing x in terms of y from the first equation, substituting it into the second equation, and solving for y, and then finding x.
Step-by-step explanation:
To solve the simultaneous equations given as 3y - x = 4 and 5y - 2x = 3, we need to find the values of x and y that satisfy both equations. Here's how we can approach solving these equations:
First, from the first equation 3y - x = 4, express x in terms of y: x = 3y - 4.
Next, substitute x = 3y - 4 from the first equation into the second equation:
5y - 2(3y - 4) = 3.
Simplify and solve for y: 5y - 6y + 8 = 3
=> -y + 8 = 3
=> y = 8 - 3
=> y = 5.
Now substitute y = 5 back into x = 3y - 4 to get the value of
x: x = 3(5) - 4
=> x = 15 - 4
=> x = 11.
The solution to the system of equations is x = 11 and y = 5.