Question

Решить методом подстановки: y+х=2; 2y-2х=5

Answer 1

$\left\{{{y+x=2}\atop{2y-2x=5}}\right.\\\left\{{{2y+2x=4}\atop{2y-2x=5}}\right.\\ \left\{{{2y=4-2x}\atop{4-2x-2x=5}}\right.\\ \left\{{{2y=4-2x}\atop{4-4x=5}}\right.\\ -4x=1\\ x=-\frac{1}{4}\\ y=2-x=2+\frac{1}{4}=2.25\\ Ans:(-0.25;2.25)$

Answer 2

Y+x=2
y=2-x
y=2-x

2y-2x=52y=5+2x
y=5/2+x
y=5/2

Answer 3

To solve the system of equations using the method of substitution, we need to first isolate one variable in one of the equations and then substitute the expression for that variable into the other equation. Let's solve the given system step-by-step:

1. y + x = 2 ............ (Equation 1)
2. 2y - 2x = 5 ......... (Equation 2)

Step 1: Solve Equation 1 for y: y = 2 - x

Step 2: Substitute the value of y (2 - x) into Equation 2: 2(2 - x) - 2x = 5

Step 3: Distribute and simplify: 4 - 2x - 2x = 5 4 - 4x = 5

Step 4: Move the constant term to the other side: -4x = 5 - 4 -4x = 1

Step 5: Solve for x: x = 1 / (-4) x = -1/4

Now that we have the value of x, we can find y by substituting the value of x back into Equation 1:

y + (-1/4) = 2

Step 6: Solve for y: y = 2 + 1/4 y = 2.25

So the solution to the system of equations is: x = -1/4 y = 2.25