1. y= -5x+2
y=3x-14
2. x+y=0
5x+y=4
3. 6x+2y=4
4x+2=8
1. subtituting we get -5x + 2 = 3x-14
so we get 8x = 16 and x=2, then plugging back in we get y = 2*-5 + 2 = -8
2. subtracting first from second equation gives us 4x = 4 so x = 1, and y = -1
3. 4x + 2 = 8 so 4x = 6, and x = 3/2
also thus 3/2*6 + 2y = 4
2y= -5
y = -5/2
maybe you had a typo and meant the second equation is 4x+2y = 8
so then we subtract frist equation from second one and get 2x = -2, x=-1
then we plug back in for the second one to get -4 + 2y = 8
y= 12/2 = 6
:D
1. since we have two expressions each equal to y, just equate them:
3x-14 = -5x+2
8x = 16
x=2
sub into one of them:
y = 3x-14 = 6-14 = -8
2. from the first : y = -x
into the 2nd:
5x -x = 4
4x=4
x = 1
then y = -1
3. probably a typo , you meant: 4x + 2y = 8
6x+2y=4
4x+2y=8
subtract them:
2x = -4
x = -2
into 4x+2y=8 ---> -8+2y=8
2y = 16
y = 8
Reiny I don't understand the second part of number 3. Please explain. Actually I really didn't understand the whole thing. Why did you subtract the two equations? than when you got the answer for x I don't even know what happened after that
3. Assuming it was a typo and the 2nd equation was 4x+2y = 8,
notice that both terms contain 2y as the y-term.
The method I used is called "elimination".
if we subtract the two equations, of course we can only add/subtract like terms, I get:
6x-4x = 2x
2y - 2y = 0 ----> Ahh, I have "eliminated" the y term
4-8 = -4
giving me
2x + 0 = -4
2x = -4
x = -2
now go back to either of the original equations, I picked the 2nd
4x+2y = 8
4(-2) + 2y = 8
-8 + 2y = 8
2y = 16
y = 8
You should try substituting x=-2 into the first, to see that you get the same answer for y.
I usually pick the easier-looking equation.
after becoming a bit more proficient in your algebra, some of those last steps can be skipped.
To solve the systems of equations given, you can use various methods such as substitution, elimination, or graphing. Let's go through each set of equations and solve them step by step.
1. y = -5x + 2 and y = 3x - 14
In this case, we can use the substitution method by setting the two expressions for y equal to each other:
-5x + 2 = 3x - 14
Now, let's solve for x. First, we'll add 5x to both sides:
2 = 8x - 14
Next, we'll add 14 to both sides:
16 = 8x
Dividing both sides by 8, we find:
x = 2
To find the value of y, substitute the value of x into one of the original equations. Let's use the second equation:
y = 3(2) - 14
y = 6 - 14
y = -8
So the solution to this system of equations is x = 2 and y = -8.
2. x + y = 0 and 5x + y = 4
We can use the elimination method in this case. By adding the two equations together, we can eliminate the y variable.
(x + y) + (5x + y) = 0 + 4
Simplifying this equation, we get:
6x = 4
Dividing both sides by 6, we find:
x = 2/3
To find the value of y, substitute the value of x into one of the original equations. Let's use the first equation:
2/3 + y = 0
y = -2/3
So the solution to this system of equations is x = 2/3 and y = -2/3.
3. 6x + 2y = 4 and 4x + 2 = 8
To solve this system, we can use the elimination method by eliminating the variable y. Multiply the second equation by 2 to make the coefficients of y equal in both equations:
6x + 2y = 4
8x + 4 = 16
Now, let's solve for x. Subtract 4 from both sides of the second equation:
8x = 12
Dividing both sides by 8, we find:
x = 3/2
Now, substitute the value of x into one of the original equations to find the value of y. Let's use the first equation:
6(3/2) + 2y = 4
9 + 2y = 4
2y = -5
y = -5/2
So the solution to this system of equations is x = 3/2 and y = -5/2.
These are the solutions to the systems of equations provided.