How do I solve theses simulations equations?y=4x-3 and y=2x-7   2x-y=-8 and 3x-y=-3  3x+2y=9 and y=x-3

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neela | High School Teacher | (Level 3) Valedictorian

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1)y=4x-3 and y=2x-7

2) 2x-y=-8 and 3x-y=-3

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

To solve the equations:

There are three pairs of simultaneous equations. Each pair of equations have(/has)  2 unknowns, x and y. We can solve the equations, by eliminating one of the unknown or by substitution and solving the for the single remaing unknown as below:

1)

y=4x-3.................(i) and

y=2x-7.................(ii) . Since right sides of both equations are equal to y, we can equate right sides and solve for x, thus eliminating x:

4x-3=2x-7 or

4x-2x=-7+3 or

2x=-4 or x=-4/2=-2. Substituting in first equation (i), we get: y=4(-2)-3= -8-3 = -11. So x=-2 and y=-11 are the solution.

2)

2x-y=-8 .................(1)and

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

eq(2)-eq(1): x = -3-(-8) = 5. So substituting x=5 in (i) ,we get,

2*5-y = -8 or -y = -8-10 or y = 18. So x= 5 and 7=18 are solutions.

3)

3x+2y=9 .....................(a) and

y=x-3..........................(b).

Substituting  y= x-3 from (b) in (a), we get:

3x+2(x-3)=9 or

3x+2x-6 = 9 or

5x=9+6 = 15 or

x=15/5 = 3. So from (b), y=x-3 = 3-3 =0 or

x = 3 and y = 0 are solutions.

 

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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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1. y=4x-3 and y=2x-7

y=4x-3 ... (1)

y=2x-7 ...(2)

Taking the value of y in (1), we put it in equation (2) to substitute the answer of x.

4x-3=2x-7

4x-2x-3=-7

2x-3=-7

2x=-7+3

2x=-4

x=-4/2

x=-2

Now, to find value of y, we put value of x into equation (1):

y=4(-2)-3

y=-8-3

y=-11

Hence, x=-2 and y=-11

2. 2x-y=-8 and 3x-y=-3

2x-y=-8 ...(1)

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

Substituting value of y from equation (1):

2x-y=-8

-y=-8-2x

Taking minus sign common on right hand side:

-y=-(8+2x)

Cancelling the minus signs:

y=8+2x

Now putting the value of y into equation (2):

3x-y=-3

3x-(8+2x)=-3

3x-8-2x=-3

x-8=-3

x=-3+8

x=5

Putting value of x in      y=8+2x

y=8+2(5)

y=8+10

y=18

Hence, x=5 and y=18

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

3x+2y=9 ... (1)

y=x-3... (2)

Since, y=x-3 in equation (1), so putting the value of y from (1), into (2),

3x+2(x-3)=9

3x+2x-6=9

5x-6=9

5x=9+6

5x=15

x=15/5

x=3

Now, putting the value of x in (2):

y=3-3

y=0

Hence, x=3, and y=0.

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