# How do you slove these simultaneous equations? Please help.1. 2y-x=-4 and x+3y=-5 2. 5y-2x=4 and 6x+y=4

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### 4 Answers

1. 2y-x=-4 and x+3y=-5

Using ELIMINATION METHOD:

2y-x=-4

-x+2y=-4 -(1)

x+3y=-5 -(2)

Hence, by using the addition method we join both equations:

-x+2y+x+3y=-4-5

-x+x+2y+3y=-9

5y=-9

**y=-9/5**

Putting the value of y in equation (1):

-x+2(-9/5)=-4

-x-18/5=-4

-5x-18 /5 = -4

-5x-18=-4*5

-5x-18=-20

-5x=-20+18

-5x=-2

x=-2/-5

**x=2/5**

2. 5y-2x=4 and 6x+y=4

Using Substitution Method:

Considering equation (2):

6x+y=4

y=4-6x

Putting value of y in equation (1):

5(4-6x) -2x = 4

20-30x-2x=4

20-32x=4

-32x=4-20

-32x=-16

x=-16/-32

x=16/32

**x=1/2**

Now, since y=4-6x,

Therefore, putting derived value of x into equation of y:

y=4-6(0.5)

y=4-3

**y=1**

For the first problem use the method of elimination. By adding the two equations together, you will cancel out the x term. Then its simple to solve for y as you normally would. Then plug this y value back into one of the original equations and solve for x.

A similar approach can be used for the second problem, but you will have to manipulate one of the equations before you add or subtract them from each other to ensure that a term cancels. For instance, you could multiply the first equation by 3 which will cancel out the x term.

1.

The two simultaneous equations are

2y - x = -4 ... (1)

x + 3y = -5 ... (2)

Adding equation (1) to equation (2) we get

x - x + 3y + 2y = - 5 - 4

Simplifying this we get:

5y = -9

Therefor y = -9/5 = -2.25

Substituting this value of y in equation (1) we get:

2*(-2.25) - x = -4

Simplifying this equation we get:

x = 0.5

Answer: x = 0.5 and y = -2.25

2.

The two simultaneous equations are:

5y - 2x = 4 ... (1)

6x + y = 4 ... (2)

Multiplying equation (1) by 3 we get:

-6x + 15y = 12 ... (3)

Adding equation (2) and (30 we get:

6x - 6x + y + 15y = 4 + 12

Simplifying this equation we get:

16y = 16

Therefore:

y = 1

Substituting this value of y in equation (1) we get:

5*1 - 2x = 4

Simplifying this equation we get:

-2x = -1

Therefor x = 1/2 = 0.5

Answer: x = 0.5 and y = 1

1)

2y-x=4..........(1)

x+3y =-5........(2)

If we add the equations, x's get cancelled and the result is:

(1)+(2) : 2y-x+x+3y = 4-5 = -1.Or

5y = -1 Or y = -1/5 = **-0.2**

From (1), 2(-1/5) -x = 4. Or

-x = 4+2/5 Or

x = -(4+2/5) =** -4.4**

**2)**

5y-2x=4 ..........(i)and

6x+y=4............(ii)

From the equation (ii), y = 4-6x, we replace y's in equation (i). So from (i), 5(4-6x)-2x=4. Or

20-30x-2x =4.Or

20-4 = 32x . Or** x** = 16/32 = 1/2 =** 0.5.**

From the (ii), 6(0.5)+y =4. Or **y** = 4-3 = **1**