Use elimination to solve the the system of equations given by 10x-4y=-20
and 10x-5y=35.
I can't figure this one out. Whenever I check my work, it is incorrect.
when I subtract the last equation from the first, I get
y = -55
sub that back into the first
10x -4(-55) = -20
10x + 220 = -20
10x = -240
x = -24
(those values verify in both equations)
Thank you! You were a lot of help!
-6x+5y=1 6x+4y=-10
To solve a system of equations using the elimination method, you need to eliminate one variable by manipulating the equations so that the coefficients of one variable are the same in both equations. Here's how you can approach this problem step by step:
Equation 1: 10x - 4y = -20
Equation 2: 10x - 5y = 35
Step 1: Multiply both sides of equation 1 by 5 and equation 2 by 4 to make the coefficients of x in both equations the same:
5(10x - 4y) = 5(-20)
4(10x - 5y) = 4(35)
This simplifies the equations to:
50x - 20y = -100
40x - 20y = 140
Step 2: Now, you can subtract equation 2 from equation 1 to eliminate the variable y:
(50x - 20y) - (40x - 20y) = (-100) - 140
The -20y and +20y terms will cancel out:
50x - 40x - 20y + 20y = -100 - 140
This simplifies to:
10x = - 240
Step 3: Divide both sides of the equation by 10 to solve for x:
10x/10 = -240/10
x = -24
Step 4: Substitute the value of x(-24) into one of the original equations and solve for y. Let's use equation 1:
10(-24) - 4y = -20
-240 - 4y = -20
-4y = -20 + 240
-4y = 220
Step 5: Divide both sides of the equation by -4 to solve for y:
-4y / -4 = 220 / -4
y = -55
So, the solution to the system of equations is x = -24 and y = -55.