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Can someone help me with all of these it’s solving systems by substitution

Can someone help me with all of these it’s solving systems by substitution-example-1

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Answer:

1. x = 0, y = 6

2. x = 2, y = -2

3. no solution

4. x = 1 - y

Explanation:

To solve by substitution, you just pick one of the two equations and solve for one of the variables. It doesn't matter which one, but I would suggest doing whatever is easiest.

Let's do it!

Example 1:

x + 5 = 5

2x + y = 6

let's solve the first equation and substitute it into the second equation

x + 5 = 5

combine like terms

x = 5 - 5

x = 0

Now we plug in 0 for x in the second equation to solve for y

2(0) + y = 6

0 + y = 6

y = 6- 0

y = 6

Final answer: x = 0, y = 6

Example 2:

2x + y = 2

2x - y = 6

let's solve Equation 1

2x + y = 2

y = 2 - 2x

Now we plug in 2 - 2x in the second equation for y

2x - y = 6

2x - (2 - 2x) = 6

4x - 2 = 6

4x = 6 + 2

4x = 8

x = 2

But we are not done yet! We don't know the exact value for y, so we are gonna take our x = 2 and plug it into the y equation

y = 2 - 2x

y = 2 - 2(2)

y = 2 - 4

y = -2

Final answer: x = 2, y = -2

Example 3:

2x + y =3

2x + y = 5

solving equation 1

y = 3 - 2x

plugging it in equation 2

2x + y = 5

2x + ( 3 - 2x ) = 5

0x + 3= 5

0x = 2x

NO SOLUTION, EXAMPLE 3 HAS NO SOLUTION AND CANNOT BE SOLVED

Example 4:

3x + 3y = 3

x + y = 1

Let's solve equation 2 instead of 1 first, because it looks easier

x + y = 1

x = 1 - y

Plug it in equation 1

3x + 3y = 3

3( 1 - y) + 3y = 3

3 - 3y + 3y = 3

3 - 0 = 3

3 = 3

This equation only has ONE SOLUTION

the solution is X = 1 - Y

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