Answer:
To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here's how to do it:
1. x + 4y = 1
2. 3x + 5y = 10
First, let's make the coefficients of x in both equations equal. We can achieve this by multiplying the first equation by 3:
3(x + 4y) = 3(1)
3x + 12y = 3
Now, we can write the system of equations again:
1. 3x + 12y = 3
2. 3x + 5y = 10
Now, we can subtract the second equation from the first equation to eliminate x:
(3x + 12y) - (3x + 5y) = 3 - 10
Simplify the equation:
7y = -7
Now, divide by 7 to solve for y:
y = -1
Now that we have the value of y, we can substitute it back into either equation to find the value of x. Let's use the first equation:
x + 4y = 1
x + 4(-1) = 1
x - 4 = 1
x = 1 + 4
x = 5
So, the solution to the system of equations is x = 5 and y = -1.
Explanation: