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Any pair of numbers where the 'y' is 5 more than the 'x'. There are an infinite number of suitable pairs.

2y-2x=10

2y-2x+2x=10+2x

2y=2x+10

divide both side by 2.

y=x+5

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2y - 2x = 10 is:

2y = 10 + 2x

2y/2 = (10 + 2x)/2

y = x + 5

-2x = -2y + 10

-2x/-2 = (-2y + 10)/-2

x = y - 5

Q: What is the solution to 2y - 2x equals 10?

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2y = -10y = -58 - 2x - 2(-5) = -108 - 2x + 10 = -10-2x = -10 - 182x = 28x = 14Check:2y = 8 - 2x - 2y = -102(-5) = 8 - 2(14) - 2(-5) = -10-10 = 8 - 28 + 10 = -10-10 = -20 + 10 = -10-10 = -10 = -10

One solution 2x+y =5 x+2y=4 multiply 1st eq by 2 rhen subtract: 4x+2y = 10 x + 2y = 4 3x = 6 x = 2 plug x into any of the above two equations and solve y = 1

y = 0 and x = 8.

Simultaneous suggests at least two equations.

16x - 2y = 74 (Eq 1) 2x - 2y = 4 (Eq 2) from Eq 2, 2y = 2x - 4 Substitute in Eq 1 16x - (2x - 4) =74 ie 16x - 2x + 4 = 74 ie 14x = 70 ie x = 5 2y = 2x - 4 = 10 - 4 = 6 y =3 Check 16 x 5 - 2 x 3 = 80 - 6 = 84 QED

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The solution is:- x = 0 and y = 5

2y = -10y = -58 - 2x - 2(-5) = -108 - 2x + 10 = -10-2x = -10 - 182x = 28x = 14Check:2y = 8 - 2x - 2y = -102(-5) = 8 - 2(14) - 2(-5) = -10-10 = 8 - 28 + 10 = -10-10 = -20 + 10 = -10-10 = -10 = -10

Divide both sides by 2: 2x = 10 - 2y __ __ ___ 2 2 2 x = 5 - y

The two equations are linear.

4x + 2y = 20 2y = -4x + 20 y = -2x + 10.......but you may also write it as y = 10 - 2x.

(12, 1)

1 solution

10-2y

-2x=2y+5 +2x -2y -2y=2x+5 /-2 y=-1/1+2.5

4x-2y = 10 -2y = -4x+10 y = 2x-5 which is now in slope-intercept form

(4, -1)

x = 3 and y = 2