Answer:
x=4 y=-1
Explanation:
To solve this system of linear equations, you can use the method of substitution or elimination. I'll use the elimination method here:
Let's first multiply the second equation by 4 to make it easier to eliminate one of the variables:
4x + 5y = 11
4(y - 3x) = 4(-13)
Now, distribute the 4 on the left side of the second equation:
4x + 5y = 11
4y - 12x = -52
Now, you can add the two equations together to eliminate the variable x:
(4x + 5y) + (4y - 12x) = 11 - 52
Combine like terms on both sides:
4x - 12x + 5y + 4y = -41
-8x + 9y = -41
Now, you have a single equation with one variable:
-8x + 9y = -41
Now, solve for one variable. Let's solve for y:
9y = -41 + 8x
9y = 8x - 41
y = (8x - 41)/9
Now that you have the expression for y, you can substitute it into one of the original equations to solve for x. I'll use the first equation:
4x + 5((8x - 41)/9) = 11
Now, you can solve for x:
4x + (40x - 205)/9 = 11
To eliminate the fraction, multiply both sides by 9:
9(4x) + 40x - 205 = 99
36x + 40x - 205 = 99
Combine like terms:
76x - 205 = 99
Now, isolate x:
76x = 99 + 205
76x = 304
Now, divide by 76:
x = 304/76
x = 4
Now that you have found the value of x, you can substitute it back into either equation to solve for y. I'll use the second equation:
y - 3(4) = -13
y - 12 = -13
Add 12 to both sides:
y = -13 + 12
y = -1
So, the solution to the system of equations is x = 4 and y = -1.