Solve the system of linear equations by elimination. Thank You for your help.
8x+10y=3
3x-5y=2
multipy the second equation by 2, then add the equations. I get
14x=7 solve for x (check that)
Ok i got that too... it comes to a fraction but then when you check it in the equations you don't get the same answer.
To solve the system of linear equations by elimination, we need to eliminate one variable by adding or subtracting the two equations.
Let's eliminate the y variable by multiplying each equation by a coefficient that will result in opposite coefficients for y.
1. Multiply the first equation by 5 and the second equation by 10 to make the coefficients of y opposite:
(5 * 8x) + (5 * 10y) = (5 * 3) --> 40x + 50y = 15
(10 * 3x) - (10 * 5y) = (10 * 2) --> 30x - 50y = 20
2. Now, add the two equations together to eliminate the y variable:
(40x + 50y) + (30x - 50y) = 15 + 20
Combine like terms: 40x + 30x + 50y - 50y = 35
Simplify: 70x = 35
3. Divide both sides of the equation by 70 to solve for x:
70x / 70 = 35 / 70
x = 0.5
4. Substitute the value of x back into one of the original equations (let's use the first equation) to solve for y:
8x + 10y = 3
Substitute x = 0.5: (8 * 0.5) + 10y = 3
4 + 10y = 3
Subtract 4 from both sides: 10y = -1
Divide both sides by 10: y = -1/10
So, the solution to the system of linear equations is x = 0.5 and y = -1/10.