Question

5(х+у)=40 21х-8у=-35

Answer 1

Ответ:

x = 8 - y

x = - 5/3 + 8/21y

Answer 2

To solve this system of linear equations for the variables x and y, you can use either the substitution method or the elimination method. I'll use the elimination method here.

Given equations:

1. 5(x + y) = 40
2. 21x - 8y = -35

Let's first simplify equation 1:

1. 5(x + y) = 40

Distribute the 5 on the left side:

5x + 5y = 40

Now, we have the system of equations:

1. 5x + 5y = 40
2. 21x - 8y = -35

To eliminate one of the variables, let's multiply equation 1 by 8 and equation 2 by 5 to make the coefficients of y in both equations equal and cancel them out:

1. (8)(5x + 5y) = (8)(40) -> 40x + 40y = 320
2. (5)(21x - 8y) = (5)(-35) -> 105x - 40y = -175

Now, the system becomes:

1. 40x + 40y = 320
2. 105x - 40y = -175

Add these two equations together to eliminate y:

(40x + 40y) + (105x - 40y) = 320 - 175

145x = 145

Now, divide both sides by 145 to solve for x:

x = 145 / 145 x = 1

Now that we have the value of x, we can substitute it into either of the original equations to solve for y. Let's use equation 1:

5x + 5y = 40 5(1) + 5y = 40 5 + 5y = 40

Subtract 5 from both sides:

5y = 40 - 5 5y = 35

Now, divide both sides by 5 to solve for y:

y = 35 / 5 y = 7

So, the solution to the system of equations is:

x = 1 y = 7