Question

10x +2y = 12-5x + 4y=-6​

Answer 1

$\left \{ {{10x+2y=12} \atop {-5x+4y=-6|*2}} \right. \Longrightarrow \left \{ {{10x+2y=12} \atop {-10x+8y=-12}} \right.$

$+\left \{ {{10x+2y=12} \atop {-10x+8y=-12}} \right. \\---------\\10y=0\\y=0\\\\10x+2*0=12\\10x=12\\x=1,2$

Ответ: (1,2; 0)

Answer 2

To solve the system of equations:

1. 10x + 2y = 12
2. -5x + 4y = -6

There are multiple ways to solve this system, but I'll use the method of substitution.

Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve equation 1 for y: 10x + 2y = 12 Subtract 10x from both sides: 2y = 12 - 10x Now, divide both sides by 2 to isolate y: y = (12 - 10x) / 2 y = 6 - 5x

Step 2: Substitute the expression for y from Step 1 into the second equation (equation 2) and solve for x. Replace y in equation 2 with (6 - 5x): -5x + 4(6 - 5x) = -6 Now, distribute the 4 on the left side of the equation: -5x + 24 - 20x = -6 Combine like terms: -25x + 24 = -6 Subtract 24 from both sides: -25x = -6 - 24 -25x = -30 Now, divide both sides by -25 to solve for x: x = -30 / -25 x = 6/5 or 1.2

Step 3: Now that we have the value of x, we can find the value of y by substituting x back into either equation 1 or the expression we derived in Step 1.

Let's use equation 1: 10x + 2y = 12 10(1.2) + 2y = 12 12 + 2y = 12 Subtract 12 from both sides: 2y = 0 Divide both sides by 2 to solve for y: y = 0

So the solution to the system of equations is x = 1.2 and y = 0.