I been stuck on this assignment since yesterday and I need some to help explain this to me and provide steps so I can come to the conclusion myself, thank you!
For problems 1-4 solve the given system of equations using either substitution or elimination.
1.{2x+y=-8
{y=2x+4
2.{10x+3y=-11
{8x+2y=-6
3.{-3x+2y=2
{3x+4y=13
4.{4x-y=-y
{-8x+4y=13
amongus isn't 100%
B
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A
D
Those are correct
5/3/2021
12:19 A.M.
1. 2x + y = -8.
y = 2x + 4.
Change Eq2 to standard form:
-2x + y = 4.
Add the Eqs:
2x + y = -8.
-2x + y = 4.
Sum = 0 + 2y = -4,
Y = -2.
In Eq1, replace Y with -2 and solve for X:
2x + (-2) = -8.
X = -3.
2. 10x + 3y = -11.
8x + 2y = -6.
Multiply Eq1 by 2 and Eq2 by 3. Then subtract Eq2 from Eq1:
20x + 6y = -22.
24x + 6y = -18.
Diff. = -4x + 0 = -4.
X = 1.
In Eq1, replace x with 1 and solve for Y:
10*1 + 3y = -11.
Y = -7.
3. -3x + 2y = 2.
3x + 4y = 13.
sum : 0 + 6y = 15.
Y =
4. 4x - y = -y.
-8x + 4y = 13.
In Eq1, solve for X:
4x - y = -y.
4x = y-y,
4x = 0,
X = 0.
In Eq2, replace X with 0 and solve for Y:
-8*0 + 4y = 13.
Y =
I will do one:
2x+y=-8
2x+2x+4=-8
4x=-12
x=-3 then y=-6+4=...
you show surprisingly little work, for having been stuck on it (and I presume trying to solve it) for two days.
Still. I'll do one, and maybe you can follow my steps for the others...
#1:
2x+y=-8
y=2x+4
substitution:
The first equation tells you that y = -2x-8
So, substitute that in the second equation, and you now have
-2x-8 = 2x+4
-4x = 12
x = -3
so, y = -2x-8 = -2
elimination. rearrange things a bit so you have
2x + y = -8
-2x + y = 4
Now, if you add the two equations, you eliminate the x, getting:
0x + 2y = -4
y = -2
so, plugging that into the 1st equation,
2x + -2 = -8
x = -3
If you have trouble, come on back, and show how far you got.
Sure! I'd be happy to help you with your assignment by explaining the steps to solve each system of equations using either substitution or elimination.
To solve a system of equations using substitution, we solve one equation for one variable and substitute it into the other equation. To solve a system of equations using elimination, we manipulate the equations to eliminate one of the variables by either adding or subtracting the equations.
Let's go through each problem step by step.
Problem 1:
{2x+y=-8
{y=2x+4
Substitution method:
Step 1: In the second equation, solve for y in terms of x. We can see that y = 2x + 4.
Step 2: Substitute the value of y from the second equation into the first equation.
2x + (2x + 4) = -8
Step 3: Simplify and solve for x.
4x + 4 = -8
4x = -12
x = -3
Step 4: Substitute the value of x back into either equation to find y.
y = 2(-3) + 4
y = -2
The solution to this system of equations is x = -3 and y = -2.
Problem 2:
{10x+3y=-11
{8x+2y=-6
Elimination method:
Step 1: Multiply the first equation by 2 and the second equation by 3 to create oppositely signed coefficients for the y term.
20x + 6y = -22
24x + 6y = -18
Step 2: Subtract the second equation from the first equation.
(20x + 6y) - (24x + 6y) = -22 - (-18)
-4x = -4
x = 1
Step 3: Substitute the value of x back into either equation to find y.
10(1) + 3y = -11
10 + 3y = -11
3y = -21
y = -7
The solution to this system of equations is x = 1 and y = -7.
Problem 3:
{-3x+2y=2
{3x+4y=13
Elimination method:
Step 1: Multiply the first equation by 2 and the second equation by 3 to create the same coefficient for the x term.
-6x + 4y = 4
9x + 12y = 39
Step 2: Add the first equation to the second equation.
(-6x + 4y) + (9x + 12y) = 4 + 39
3x + 16y = 43
Step 3: Solve the resulting equation for x or y. Let's solve for x.
3x = 43 - 16y
Step 4: Substitute the value of x back into the first equation to find y.
-3(43 - 16y) + 2y = 2
-129 + 48y + 2y = 2
50y = 131
y ≈ 2.62
Step 5: Substitute the value of y back into either equation to find x.
-3x + 2(2.62) = 2
-3x + 5.24 = 2
-3x = -3.24
x ≈ 1.08
The solution to this system of equations is x ≈ 1.08 and y ≈ 2.62.
Problem 4:
{4x-y=-y
{-8x+4y=13
Substitution method:
Step 1: In the first equation, solve for x in terms of y. We can see that 4x = 0y. Since the coefficient of y is the same on both sides, the equation is satisfied for every value of y. Therefore, we can say x = k, where k is any real number.
Step 2: Substitute the value of x = k back into either equation to find y.
-8k + 4y = 13
4y = 13 + 8k
y = (13 + 8k)/4
y = (13/4) + 2k
The solution to this system of equations is x = k and y = (13/4) + 2k, where k is any real number.
I hope this explanation helps you understand how to solve systems of equations using substitution or elimination! If you have any further questions, feel free to ask.
B
C
D
D