use either substitution or elimination to solve
8x+15y=13
2x-5y=-1
Multiply the 2nd equation by 3 and you'll get 6x - 15y = -3 "Add" this equation to the 1st equation and you eliminate the y variable and get 14x = 10.Therefore, x = 5/7. Substitute this into one of the original equations and solve for y.
To solve the system of equations using substitution or elimination, we can follow these steps:
Substitution Method:
1. Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for x:
2x - 5y = -1
2x = 5y -1
x = (5y - 1)/2
2. Substitute the expression for the solved variable into the other equation.
Substituting x in the first equation:
8((5y - 1)/2) + 15y = 13
Simplifying, we have:
4(5y - 1) + 15y = 13
20y - 4 + 15y = 13
35y - 4 = 13
35y = 17
y = 17/35
3. Substitute the value of y back into one of the original equations to solve for x.
Let's use the second equation:
2x - 5(17/35) = -1
Simplifying, we have:
2x - 85/35 = -1
2x - 17/7 = -1
2x = -7/7 + 17/7
2x = 10/7
x = 10/7 * (1/2)
x = 10/14
x = 5/7
The solution to the system of equations is x = 5/7 and y = 17/35.
Elimination Method:
1. Multiply one or both equations by suitable constants to make the coefficients of one of the variables the same (or additive inverses).
Let's multiply the first equation by 2:
2(8x + 15y) = 2(13)
16x + 30y = 26
2. Add the resulting equations to eliminate one variable.
(16x + 30y) + (2x - 5y) = 26 + (-1)
16x + 2x + 30y - 5y = 25
18x + 25y = 25
3. Solve the resulting equation for one variable.
Simplifying, we have:
18x + 25y = 25
18x = 25 - 25y
x = (25 - 25y)/18
4. Substitute the expression for the solved variable back into one of the original equations to solve for the other variable.
Substituting x in the first equation:
8((25 - 25y)/18) + 15y = 13
Simplifying, we have:
(8(25 - 25y) + 15y)/18 = 13
(200 - 200y + 15y)/18 = 13
(200 - 185y)/18 = 13
200 - 185y = 13*18
200 - 185y = 234
-185y = 234 - 200
-185y = 34
y = 34/(-185)
y = -2/11
5. Substitute the value of y back into one of the original equations to solve for x.
Using the second equation:
2x - 5(-2/11) = -1
Simplifying, we have:
2x + 10/11 = -1
2x = -1 - 10/11
2x = -11/11 - 10/11
2x = -21/11
x = -21/11 * (1/2)
x = -21/22
The solution to the system of equations using the elimination method is x = -21/22 and y = -2/11.