Question

Система y-3x=-5 2y+5x=23

Answer 1

Сделал правильно на все 100%

Answer 2

To solve the system of equations y-3x=-5 and 2y+5x=23, we can use either the substitution method or the elimination method. I'll demonstrate both methods so you can choose the one you prefer.

Method 1: Substitution Method

Step 1: Solve one of the equations for one variable (preferably y or x). Step 2: Substitute the expression from Step 1 into the other equation. Step 3: Solve for the remaining variable. Step 4: Once you have the value of one variable, substitute it back into either equation to find the other variable.

Let's use the first equation, y-3x=-5, to solve for y:

Step 1: y = 3x - 5

Now, substitute this value of y into the second equation, 2y + 5x = 23:

Step 2: 2(3x - 5) + 5x = 23 Step 3: 6x - 10 + 5x = 23 Step 4: 11x - 10 = 23 Step 5: 11x = 23 + 10 Step 6: 11x = 33 Step 7: x = 33 / 11 Step 8: x = 3

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

y = 3(3) - 5 y = 9 - 5 y = 4

So the solution to the system of equations is x = 3 and y = 4.

Method 2: Elimination Method

Step 1: Multiply one or both equations by appropriate constants so that the coefficients of either x or y will cancel out when added together. Step 2: Add or subtract the modified equations to eliminate one variable. Step 3: Solve for the remaining variable. Step 4: Once you have the value of one variable, substitute it back into either equation to find the other variable.

Let's use the elimination method to solve the system of equations:

Step 1: We'll multiply the first equation, y - 3x = -5, by 2 to eliminate y when added to the second equation.

2(y - 3x) = 2(-5) 2y - 6x = -10

Now, the system becomes:

2y - 6x = -10 2y + 5x = 23

Step 2: Subtract the first equation from the second equation to eliminate y:

(2y + 5x) - (2y - 6x) = 23 - (-10) 2y + 5x - 2y + 6x = 23 + 10 11x = 33 x = 33 / 11 x = 3

Step 3: Now that we have the value of x, substitute it back into the first equation to find y:

y - 3(3) = -5 y - 9 = -5 y = -5 + 9 y = 4

So, the solution to the system of equations is x = 3 and y = 4, which matches the result we obtained using the substitution method.