Question

1. 9х+y=26 4x+3y=9 2. 5x-y=-32 7x+6y=-30 3. -5x+6y=46 5x+y=-4 4. 7x+9y=-24 -7x-y=40

Answer 1

Пошаговое объяснение:

1. 9х+y=26

4x+3y=9

у=26-9х

4х+3*(26-9х)=9

у=26-9х

4х+78-27х=9

у=26-9х

4х-27х=9-78

у=26-9х

23х=69

у=26-9х

х=3

у=26-9*3

х=3

у=-1

х=3

2. 5x-y=-32

7x+6y=-30

у=32+5х

7х+6*(32+5х)=-30

у=32+5х

7х+192+30х=-30

у=32+5х

37х=-222

у=32+5х

х=4

у=52

х=4

3. -5x+6y=46

5x+y=-4

-5х+6у=46

у=-4-5х

-5х+6*(-4-5х)=46

у=-4-5х

-5х-24-30х=46

у=-4-5х

-35х=70

у=-4-5х

х=-2

у=6

4. 7x+9y=-24

-7x-y=40

7х+9у=-24

у=-40-7х

7х+9*(-40-7х)=-24

у=-40-7х

7х-360-63х=-24

у=-40-7х

-56х=336

у=-40-7х

х=-6

у=2

Answer 2

To solve these systems of linear equations, we can use various methods such as substitution, elimination, or matrix methods. I'll use the substitution method to solve each system.

1. 9x + y = 26 4x + 3y = 9

Let's solve for y in the first equation: y = 26 - 9x

Now, substitute the value of y in the second equation: 4x + 3(26 - 9x) = 9 4x + 78 - 27x = 9 -23x + 78 = 9 -23x = 9 - 78 -23x = -69 x = -69 / -23 x = 3

Now that we have x, substitute it back into the first equation to find y: 9(3) + y = 26 27 + y = 26 y = 26 - 27 y = -1

So the solution to the first system is x = 3 and y = -1.

2. 5x - y = -32 7x + 6y = -30

Let's solve for y in the first equation: y = 5x + 32

Now, substitute the value of y in the second equation: 7x + 6(5x + 32) = -30 7x + 30x + 192 = -30 37x + 192 = -30 37x = -30 - 192 37x = -222 x = -222 / 37 x = -6

Now that we have x, substitute it back into the first equation to find y: 5(-6) - y = -32 -30 - y = -32 y = -32 + 30 y = -2

So the solution to the second system is x = -6 and y = -2.

3. -5x + 6y = 46 5x + y = -4

Let's solve for y in the second equation: y = -4 - 5x

Now, substitute the value of y in the first equation: -5x + 6(-4 - 5x) = 46 -5x - 24 - 30x = 46 -35x - 24 = 46 -35x = 46 + 24 -35x = 70 x = 70 / -35 x = -2

Now that we have x, substitute it back into the second equation to find y: 5(-2) + y = -4 -10 + y = -4 y = -4 + 10 y = 6

So the solution to the third system is x = -2 and y = 6.

4. 7x + 9y = -24 -7x - y = 40

Add both equations together to eliminate x: (7x + 9y) + (-7x - y) = -24 + 40 7y = 16 y = 16 / 7

Now that we have y, substitute it back into either equation to find x. Let's use the first equation: 7x + 9(16 / 7) = -24 7x + 144 / 7 = -24 7x = -24 - 144 / 7 7x = (-168 - 144) / 7 7x = -312 / 7 x = -312 / 7 * 1/7 x = -312 / 49

So the solution to the fourth system is x = -312 / 49 and y = 16 / 7.