12x+16y=1/5 and 13x+14y=1/4
Find the x, y value
I would use elimination:
multiply the first by 13
and the second by 12 to get the same x terms
then subtract them to solve for y
then sub back into the first to get the x
hint: answers are exact fractions.
To find the values of x and y that satisfy the given system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method:
1. Multiply the first equation by 20 and the second equation by 25 to eliminate the fractions:
240x + 320y = 4
325x + 350y = 5
2. Now we can eliminate one variable by subtracting the two equations:
(325x + 350y) - (240x + 320y) = 5 - 4
85x + 30y = 1
3. Solve the resulting equation for one variable in terms of the other. In this case, let's solve it for x:
85x = 1 - 30y
x = (1 - 30y) / 85
4. Substitute this value of x into one of the original equations. Let's use the first equation:
12x + 16y = 1/5
12((1 - 30y) / 85) + 16y = 1/5
5. Simplify the equation and solve for y:
Multiply through by 85 to eliminate the fractions:
12(1 - 30y) + 85(16y) = 17
12 - 360y + 1360y = 17
-348y = 5
y = -5/348
6. Substitute this value of y back into the equation we found in step 3 to find x:
x = (1 - 30y) / 85
x = (1 - 30(-5/348)) / 85
x = 31/348
So the solution to the system of equations is x = 31/348 and y = -5/348.