how do yu solve 6y-4z=-2 and 4y+6z=42 using additon method show all steps
eliminating a variable using the addition method.
1) 6y - 4z = -2
2) 4y + 6z = 42
Because the z terms have opposite signs, we can eliminate
the z if they have the same co-efficient. 12 is the choice.
Multiply each equation by a number that gives the co-efficient
we want.
Equation 1:
3 * (6y - 4z) = -2 * 3
3) 18y - 12z = -6
Equation 2:
2 * (4y + 6z) = 42 * 2
4) 8y + 12z = 84
Now, add equations 3 and 4.
18y - 12z = -6
+(8y + 12z = 84)
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26y = 78
26y = 78
y = 78/26
y = 3
Use that in either equation 1 or equation 2 to solve for z.
4y + 6z = 42
4(3) + 6z = 42
12 + 6z = 42
12 + 6z - 12 = 42 - 12
6z = 30
z = 30 / 6
z = 5
Answer: y = 3, z = 5