these questions are:
ELIMINATION USING MULTIPLICATION:
1. 2.
2x + 5y = 3 2x + y = 3
-x + 3y =-7 5x + 3y = 2
I NEED HELP ASAP!!!!
HELP PLEASE!!!!
If I were you, I would mutiply the bottom left clear through by 2 to get rid of the x's and leave the y's:
2x+5y=3
-2x+6y=-14
2+-2 opposites add up to zero
11y=-11
y=-1
Do the same with the others on the right. -3 as a factor makes the y's go away so you have nothing but x's to do.
-6x+-3y=-9 and 5x+3y=2 Opposite 3's add up to zero.
-x=-7 which is the same as x=7
Introduce a factor that gives you only one variable letter to work with instead of two. Take -x times 2 to get -2x which adds up to zero when added to 2x. Boom, your x's are gone. Solve for y and use whatever y equals to find x back in the original equations. -3y+3y=0 for the other side, so you can knock out the y's. Figure out x. Go back and figure out y based upon x.
thnx i got the answers to that one but now im stuck on elimination using addition and subtraction.
To solve these systems of equations using elimination, you can multiply one or both equations by specific numbers so that the coefficients of one of the variables will cancel each other out when the equations are added together. Here's how you can solve each question step by step:
1. 2x + 5y = 3 (Equation 1)
-x + 3y = -7 (Equation 2)
To use the elimination method, you can see that if Equation 1 is multiplied by 3 and Equation 2 is multiplied by 2, the coefficients of x in both equations will be equal and opposite: -3x and -2x.
Multiply Equation 1 by 3:
3(2x + 5y) = 3(3)
6x + 15y = 9 (Equation 1 multiplied by 3)
Multiply Equation 2 by 2:
2(-x + 3y) = 2(-7)
-2x + 6y = -14 (Equation 2 multiplied by 2)
Now, you can add the two equations together, eliminating the x variable:
(6x + 15y) + (-2x + 6y) = 9 + (-14)
6x + (-2x) + 15y + 6y = 9 - 14
4x + 21y = -5
You have now eliminated the x variable from the equations and obtained a single equation in terms of y.
2. 2x + y = 3 (Equation 1)
5x + 3y = 2 (Equation 2)
To use the elimination method, you can see that if Equation 1 is multiplied by 5 and Equation 2 is multiplied by 2, the coefficients of y in both equations will be equal and opposite: 5y and -6y.
Multiply Equation 1 by 5:
5(2x + y) = 5(3)
10x + 5y = 15 (Equation 1 multiplied by 5)
Multiply Equation 2 by 2:
2(5x + 3y) = 2(2)
10x + 6y = 4 (Equation 2 multiplied by 2)
Now, you can subtract the two equations, eliminating the y variable:
(10x + 5y) - (10x + 6y) = 15 - 4
10x - 10x + 5y - 6y = 15 - 4
-y = 11
You have now eliminated the y variable from the equations and obtained a single equation in terms of x.
Now, for both questions, you can use the obtained equation to solve for the remaining variable:
1. Solve for y:
4x + 21y = -5
21y = -5 - 4x
y = (-5 - 4x) / 21
2. Solve for x:
-y = 11
y = -11
From Equation 1:
2x + (-11) = 3
2x = 3 + 11
2x = 14
x = 14 / 2
x = 7
For question 1, y can be expressed as (-5 - 4x) / 21 and x = 7.
For question 2, x = 7 and y = -11.
I hope this helps! Let me know if you have any further questions.