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4 years ago

Can someone please help me solve this system of equations

Mathematics

1 answer:

sergejj [24]4 years ago

4 0

Answer:

x=15 and y=2

Step-by-step explanation:

The given system of equations is

8y - x = 1 ...............(i)

and

10 y = x + 5 ...............(ii)

Now from equation (ii)

10 y = x + 5

subtracting -5 from both sides

10 y - 5 = x + 5 - 5

10 y -5 = x

x = 10y -5 ............(iii)

Put this in equation (i)

it becomes

8y - (10y -5) = 1

8y-10y+5=1

-2y+5 =1

subtracting 5 from both sides

-2y + 5 -5 = 1 -5

-2y = -4

dividing both sides by -2 gives

-2y / -2 = -4 / -2

y = 2

We got the value of y putting it in equation (iii) to get the value of x

as from equation (iii)

x = 10y-5

x = 10(2) - 5

x = 20 -5

x = 15

So this is the solution from the equations

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Art [367]

Answer:

g = 10.82

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-1.9

Step-by-step explanation:

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3 years ago

The graph of y > 1 2 x - 2 is shown. Which set contains only points that satisfy the inequality? A) {(6, 1), (-1, -3), (4, 4)

Kaylis [27]

Answer:

Option B) {(1, -1), (-3, -3), (2, 4)}

Step-by-step explanation:

The correct inequality is

$y>\frac{1}{2}x-2$

The solution of the inequality is the shaded area above the dashed line $y=\frac{1}{2}x-2$

see the attached figure to better understand the problem

we know that

If a ordered pair satisfy the inequality, then the ordered pair must lie in the shaded area of the solution

Verify each case

case A) {(6, 1), (-1, -3), (4, 4)}

ordered pair (6,1)

For x=6, y=1

substitute in the inequality

$1>\frac{1}{2}(6)-2$

$1>1$ ---> is not true

therefore

The point not satisfy the inequality

case B) {(1, -1), (-3, -3), (2, 4)}

ordered pair (1,-1)

For x=1, y=-1

substitute in the inequality

$-1>\frac{1}{2}(1)-2$

$-1>-1.5$ ---> is true

The point satisfy the inequality

ordered pair (-3,3)

For x=-3, y=3

substitute in the inequality

$3>\frac{1}{2}(-3)-2$

$3>-3.5$ ---> is true

The point satisfy the inequality

ordered pair (2,4)

For x=2, y=4

substitute in the inequality

$4>\frac{1}{2}(2)-2$

$4>-1$ ---> is true

The point satisfy the inequality

therefore

The set contains only points that satisfy the inequality

case C) {(1, -1), (-3, -3), (4, -2)}

ordered pair (4,-2)

For x=4, y=-2

substitute in the inequality

$-2>\frac{1}{2}(4)-2$

$-2>0$ ---> is not true

therefore

The point not satisfy the inequality

case D) {(-1, -3), (-3, -3), (2, 4)}

ordered pair (-1,-3)

For x=-1, y=-3

substitute in the inequality

$-3>\frac{1}{2}(-1)-2$

$-3>-2.5$ ---> is not true

therefore

The point not satisfy the inequality

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3 years ago

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4 years ago

A candy store owner wants to mix some candy costing $1.25 a pound

maria [59]

The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.

Given:

Candy costing $1.25 a pound is to be mixed with candy costing $1.45 a pound
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To find: The amount of candy costing $1.25 a pound that should be mixed

Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.

Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with ' $50-x$ ' pounds of candy costing $1.45 a pound.

Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and ' $50-x$ ' pounds of candy costing $1.45 a pound.

Accordingly, the total cost of the resulting mixture is $1.25x+1.45(50-x)$

However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is $1.30 \times 50$