Question

3(4x - 2y+1)-2(5x-y+4)= 23 2(x + 6 - 9) + 5(2x - 4y + 7) = 105

Answer 1

12х-6у+3-10х+2у-8=23
2х-4у-5=23
2х-4у=28

Answer 2

To solve the given system of equations, we'll start by simplifying each equation step by step and then solving for the variables. Let's go through it:

1. Equation 1: 3(4x - 2y + 1) - 2(5x - y + 4) = 23 First, distribute the numbers outside the parentheses: 12x - 6y + 3 - 10x + 2y - 8 = 23 Combine like terms: (12x - 10x) + (-6y + 2y) + (3 - 8) = 23 2x - 4y - 5 = 23 Now, isolate the variables on one side by moving the constant term to the other side: 2x - 4y = 23 + 5 2x - 4y = 28

2. Equation 2: 2(x + 6 - 9) + 5(2x - 4y + 7) = 105 First, simplify inside the parentheses: 2(x - 3) + 5(2x - 4y + 7) = 105 Distribute the numbers outside the parentheses: 2x - 6 + 10x - 20y + 35 = 105 Combine like terms: (2x + 10x) + (-6 - 20y + 35) = 105 12x - 20y + 29 = 105 Now, isolate the variables on one side by moving the constant term to the other side: 12x - 20y = 105 - 29 12x - 20y = 76

Now we have the following system of equations:

1. 2x - 4y = 28
2. 12x - 20y = 76

We can solve this system by using either the substitution method or the elimination method. Let's use the elimination method:

1. Multiply equation 1 by 5 and equation 2 by 1 to make the coefficients of y in both equations equal: 5(2x - 4y) = 5(28) => 10x - 20y = 140 1(12x - 20y) = 1(76) => 12x - 20y = 76

2. Subtract the modified equation 2 from the modified equation 1 to eliminate y: (10x - 20y) - (12x - 20y) = 140 - 76 10x - 20y - 12x + 20y = 64 -2x = 64

3. Divide by -2 to solve for x: x = 64 / -2 x = -32

4. Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation 1: 2x - 4y = 28 2(-32) - 4y = 28 -64 - 4y = 28

5. Now, isolate y by moving the constant term to the other side: -4y = 28 + 64 -4y = 92

6. Divide by -4 to solve for y: y = 92 / -4 y = -23

So, the solution to the system of equations is x = -32 and y = -23.