Answer:
Sophie has 12.5 cards
Step-by-step explanation:
Let
x -----> number of cards Sophie has
y -----> number of cards Jackie has
we know that
x+y=30 -----> equation A
y=x+5 -----> equation B
Solve by substitution
Substitute equation B in equation A and solve for x
x+(x+5)=30
2x=30-5
x=12.5 cards
Note I assume the problem was invented without taking into account the result, because the amount of cards should be a whole number
There are many ways to solve simultaneous linear equations. One of my favorite for finding integer solutions is graphing. The attached graph shows the solution to be ...
... (x, y) = (4, 7)
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You can also use Cramer's Rule, or the Vedic math variation of it, which tells you the solution to

is given by

Here, that means
... x = (9·67-5·75)/(9·8-5·3) = 228/57 = 4
... y = (75·8-67·3)/57 = 399/57 = 7
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A (graphing) calculator greatly facilitates either of these approaches.
Answer:
If the expression is:
-3x + 12 = -3x + 12, infinite solutions
If the expression is:
-3x + 12 = -3x - 12, no solutions
Step-by-step explanation:
Step 1: Distribute
-3x + 12 = 3x = 12
If both lines have the same slope and same y-int, they are the same line and therefore have infinite solutions.
If both lines have the same slope but different y-int, then they are parallel and therefore have no solutions.