I'll just do 5 and 8 for you:
5) y= x+3
3x+ 2y= 26
Copy the second equation, but instead of y, don't
write y, but instead write what y equals from the
first equation, which is x+3 in parentheses (x+3)
3x+ 2(x+3)= 26
Remove parentheses by distributing
3x + 2x + 6 = 26
5x + 6 = 26
5x = 20
x = 4
Substitute (4) for x in y= x+3
y= 4+3
y = 7
Solution: (x,y) = (4,7)
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8) 2x+3y= 7
4x-5y= 25
We notice that the second equation has 4x and the first
equation has 2x, and we know that 4x is 2 times 2x
So we solve the first equation for 2x
2x+3y= 7
We subtract 3y from both sides
2x= 7-3y
We need 4x, not 2x, to substitute in the second equation,
so we multiply both sides, every term, of that equation by 2:
4x= 14-6y
Copy the second equation, 4x-5y= 25 but instead of 4x,
don't write 4x, but instead write what 4x equals from that
equation, which is 14-6y.
14-6y-5y= 25
Combine like terms
14-11y = 25
Add -14 to both sides:
-11y = 11
y = -1
Solution: (x,y) = (5,-1)
Edwin
