8x + 14y = 24
6x + 7y = 10
We are suppose to solve for x and y but I don't get the right answer
so why don't you show us what you did? One way is to notice that 14 = 7*2, so if we double the 2nd equation, we get
8x + 14y = 24
12x + 14y = 20
Now if we subtract the equations, the y's cancel out, and we get
-4x = 4
x = -1
Now use that in either equation to get y.
8(-1)+14y = 24
-8+14y = 24
14y = 32
y = 16/7
To solve the system of equations, you can use the method of substitution or the method of elimination. Let's use the method of substitution.
First, solve one equation for one variable and substitute it into the other equation. Let's solve the second equation for x:
6x + 7y = 10
Rearrange the equation to isolate x:
6x = 10 - 7y
x = (10 - 7y)/6
Now substitute this expression for x into the first equation:
8((10 - 7y)/6) + 14y = 24
Next, simplify the equation:
(80 - 56y)/6 + 14y = 24
Multiply both sides of the equation by 6 to eliminate the denominator:
80 - 56y + 84y = 144
Combine like terms:
80 + 28y = 144
Subtract 80 from both sides:
28y = 144 - 80
28y = 64
Divide both sides by 28:
y = 64/28
y = 8/7
Now substitute this value of y back into the expression for x:
x = (10 - 7(8/7))/6
Simplify:
x = (10 - 8)/6
x = 2/6
Simplify further:
x = 1/3
Therefore, the solution to the system of equations is x = 1/3 and y = 8/7.