Question

A) 2x + 3y = 5, 4x - 3y = -3; б) 4x + 3y = 11, 4x - 3y = - 3.

Answer 1

Ответ:

а) х=1/3 б)у=7/3=2 1/3

у=13/9=1 4/9 х=1

решение на фото)

Answer 2

To solve the systems of equations, we can use the method of elimination or substitution. I'll demonstrate both methods for each system:

A) 2x + 3y = 5, 4x - 3y = -3:

Method 1: Elimination Step 1: Add the two equations to eliminate the y variable. (2x + 3y) + (4x - 3y) = 5 - 3 6x = 2 Step 2: Solve for x x = 2/6 x = 1/3

Step 3: Substitute the value of x into one of the original equations to find y: 2(1/3) + 3y = 5 2/3 + 3y = 5 3y = 5 - 2/3 3y = 15/3 - 2/3 3y = 13/3 y = 13/3 * 1/3 y = 13/9

So, the solution to the system is x = 1/3 and y = 13/9.

Method 2: Substitution Step 1: Solve one of the equations for one variable, let's say the first equation for y: 2x + 3y = 5 3y = 5 - 2x y = (5 - 2x)/3

Step 2: Substitute this expression for y into the second equation: 4x - 3((5 - 2x)/3) = -3 4x - (5 - 2x) = -3 4x - 5 + 2x = -3 6x - 5 = -3 6x = -3 + 5 6x = 2 x = 2/6 x = 1/3

Step 3: Substitute the value of x back into the expression for y from step 1: y = (5 - 2(1/3))/3 y = (5 - 2/3)/3 y = (15/3 - 2/3)/3 y = 13/9

So, the solution to the system is x = 1/3 and y = 13/9.

B) 4x + 3y = 11, 4x - 3y = -3:

Method 1: Elimination Step 1: Add the two equations to eliminate the y variable. (4x + 3y) + (4x - 3y) = 11 - 3 8x = 8 Step 2: Solve for x x = 8/8 x = 1

Step 3: Substitute the value of x into one of the original equations to find y: 4(1) + 3y = 11 4 + 3y = 11 3y = 11 - 4 3y = 7 y = 7/3

So, the solution to the system is x = 1 and y = 7/3.

Method 2: Substitution Step 1: Solve one of the equations for one variable, let's say the first equation for y: 4x + 3y = 11 3y = 11 - 4x y = (11 - 4x)/3

Step 2: Substitute this expression for y into the second equation: 4x - 3((11 - 4x)/3) = -3 4x - (11 - 4x) = -3 4x - 11 + 4x = -3 8x - 11 = -3 8x = -3 + 11 8x = 8 x = 8/8 x = 1

Step 3: Substitute the value of x back into the expression for y from step 1: y = (11 - 4(1))/3 y = (11 - 4)/3 y = 7/3

So, the solution to the system is x = 1 and y = 7/3.