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41. Solve the simultaneous equations:
[tex]\[ 3x - y = 5 \][/tex]
[tex]\[ x + y = 7 \][/tex]

The values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
a) [tex]\( (3, 2) \)[/tex]
b) [tex]\( (3, 5) \)[/tex]
c) [tex]\( (2, 4) \)[/tex]
d) [tex]\( (3, 4) \)[/tex]

42. Evaluate the expression:
[tex]\[ |2| + |3| - |-5| + |-4| - |-2| \][/tex]

The value is:
a) 1
b) 3
c) 4
d) 2

Sagot :

GinnyAnswer
Certainly! Let's solve these questions step by step.

### Question 41
We are given the simultaneous equations:
[tex]\[ 3x - y = 5 \][/tex]
[tex]\[ x + y = 7 \][/tex]

We need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

Step 1: Solve the second equation for [tex]\( y \)[/tex].
[tex]\[ x + y = 7 \][/tex]
[tex]\[ y = 7 - x \][/tex]

Step 2: Substitute the expression for [tex]\( y \)[/tex] into the first equation.
[tex]\[ 3x - (7 - x) = 5 \][/tex]
[tex]\[ 3x - 7 + x = 5 \][/tex]
[tex]\[ 4x - 7 = 5 \][/tex]

Step 3: Solve for [tex]\( x \)[/tex].
[tex]\[ 4x = 12 \][/tex]
[tex]\[ x = 3 \][/tex]

Step 4: Substitute [tex]\( x = 3 \)[/tex] back into the expression for [tex]\( y \)[/tex]
[tex]\[ y = 7 - x \][/tex]
[tex]\[ y = 7 - 3 \][/tex]
[tex]\[ y = 4 \][/tex]

So, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
[tex]\[ x = 3, \; y = 4 \][/tex]

Thus, the correct option is:
d) [tex]\((3, 4)\)[/tex]

### Question 42
We need to evaluate the expression:
[tex]\[ |2| + |3| - |-5| + |-4| - |-2| \][/tex]

Step 1: Evaluate the absolute values.
Absolute values convert any number to its non-negative form.
[tex]\[ |2| = 2 \][/tex]
[tex]\[ |3| = 3 \][/tex]
[tex]\[ |-5| = 5 \][/tex]
[tex]\[ |-4| = 4 \][/tex]
[tex]\[ |-2| = 2 \][/tex]

Step 2: Substitute these values into the expression.
[tex]\[ 2 + 3 - 5 + 4 - 2 \][/tex]

Step 3: Perform the addition and subtraction step by step.
[tex]\[ 2 + 3 = 5 \][/tex]
[tex]\[ 5 - 5 = 0 \][/tex]
[tex]\[ 0 + 4 = 4 \][/tex]
[tex]\[ 4 - 2 = 2 \][/tex]

Thus, the value of the expression is:
d) 2

Summary of the answers:
41. d) [tex]\((3, 4)\)[/tex]
42. d) 2
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