A student is trying to solve the set of two equations given below:
Equation A: x + z = 6
Equation B: 2x + 4z = 1
Which of the following is a possible step used in eliminating the z-term?
Multiply equation B by 4.
Multiply equation A by 2.***
Multiply equation A by −4.***
Multiply equation B by 2.
(either b or c)
b would be used to eliminate x
but
you are supposed to eliminate z
so
c
which would give you -4z+4z = 0
The correct possible step used in eliminating the z-term is to multiply equation A by −4.
To eliminate the z-term in the given set of equations, you need to perform some operations on the equations so that when you add or subtract them, the z-term cancels out.
In this case, you want to eliminate the z-term. Looking at the possible steps given, you can determine if multiplying equation A by 2 or multiplying equation A by -4 would achieve this.
If you multiply equation A by 2, the resulting equation would be:
2(x + z) = 2(6)
2x + 2z = 12
Notice that the z-term is still present, so multiplying equation A by 2 does not eliminate the z-term.
If you multiply equation A by -4, the resulting equation would be:
-4(x + z) = -4(6)
-4x - 4z = -24
Here, the z-term has been affected by the multiplication, and it has become -4z. In this case, the negative sign is important because we are trying to eliminate the z-term. So multiplying equation A by -4 does eliminate the z-term.
Therefore, the correct answer is c) Multiply equation A by -4.