Q1. Solve the system of equationd by addition method.
-2x+y=6
-3x-4y=20
Select the correct choice below and, if necessary, fill in the answer box to comlete your choice
a)The solution is__(simplify your answer. type an ordere pair)
b) Infinitely many solutions
c) No Solution
Q2. Solve the system of equationd by addition method.
6x+4y=-10
2x-4y=-30
Select the correct choice below and, if necessary, fill in the answer box to comlete your choice
a)The solution is__(simplify your answer. type an ordere pair)
b) Infinitely many solutions
c) No Solution
Q3. Solve the system of equationd by addition method.
2x+4y=7
4x+8y=0
Select the correct choice below and, if necessary, fill in the answer box to comlete your choice
a)The solution is__(simplify your answer. type an ordere pair)
b) Infinitely many solutions
c) No Solution
Q4. Solve the system of equationd by addition method.
-2x=-2y-8
-4x+2y=-16
Select the correct choice below and, if necessary, fill in the answer box to comlete your choice
a)The solution is__(simplify your answer. type an ordere pair)
b) Infinitely many solutions
c) No Solution
Q5. Solve the system of equationd by addition method.
-3x-5y=7
5x+15y=7
The solution is ___
Q6. Solve the system of equationd by addition method.
(x/2)-(y/6)=-1
(x/4)+(y/12)=-3
Select the correct choice below and, if necessary, fill in the answer box to comlete your choice
a)The solution is__(simplify your answer. type an ordere pair)
b) Infinitely many solutions
c) No Solution
Q7. Solve the system of equationd by addition method.
(x/7)-y=2
-(x/2)+(7y/2)=-7
Select the correct choice below and, if necessary, fill in the answer box to comlete your choice
a)The solution is__(simplify your answer. type an ordere pair)
b) Infinitely many solutions
c) No Solution
Q8.Solve the system of equationd by addition method or the substitution method
x+(1/20y)=(1/4)
3x+2y=2
The solution is ______
Well, actually, we do often do the homework. However, it's a bit daunting to get a whole problem set dumped out, especially when all the problems are similar. I'll do Q6 to get you started. It is complicated enough that its solution should help you with the others.
(x/2)-(y/6)=-1
(x/4)+(y/12)=-3
Some people revel in working with fractions, but I find them a burden. So, get rid of all those nasty denominators. Multiply the first equation by 6, and the second by 12:
3x - y = -6
3x + y = -36
Now, add these equations and something magic happens -- the y's go away:
6x = -42
x = -7
Now, using either of the two equations, we can find y:
3x - y = -6
3(-7) - y = -6
-21 - y = -6
-y = 15
y = -15
Now, check to make sure your answer fits both of the original equations:
(x/2)-(y/6)=-1
-7/2 - (-15/6) = -1
-7/2 + 5/2 = -1
-2/2 = -1
-1 = -1
(x/4)+(y/12)=-3
-7/4 + (-15/12) = -3
-7/4 - 5/4 = -3
-12/4 = -3
-3 = -3
To solve the system of equations by addition method, follow these steps:
Step 1: Ensure that the coefficients of one of the variables in both equations are equal in magnitude but opposite in sign.
Step 2: Add or subtract the two equations to eliminate one variable.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value of the variable found in step 3 back into one of the original equations to solve for the other variable.
Now let's solve the given systems of equations:
Q1. Solve the system of equations by addition method:
-2x + y = 6 ...(Equation 1)
-3x - 4y = 20 ...(Equation 2)
To eliminate x, we can multiply Equation 1 by 3 and Equation 2 by -2, so that the coefficients of x will be equal:
(3)(-2x + y) = (3)(6)
(-2)(-3x - 4y) = (-2)(20)
This simplifies to:
-6x + 3y = 18 ...(Equation 3)
6x + 8y = -40 ...(Equation 4)
Now, add Equation 3 and Equation 4 to eliminate x:
(-6x + 3y) + (6x + 8y) = 18 + (-40)
11y = -22
Divide both sides of the equation by 11:
y = -2
Now we substitute the value of y back into Equation 1 to solve for x:
-2x + (-2) = 6
-2x - 2 = 6
-2x = 6 + 2
-2x = 8
Divide both sides of the equation by -2:
x = -4
The solution is (-4, -2).
Therefore, the correct choice for Q1 is a) The solution is (-4, -2).
Now you can apply the same steps to solve the remaining questions.