3x=5y
6x-7y=17
Using Elimination Method (?)
Find x and y
To solve the given system of equations using the Elimination Method, you need to eliminate one variable (either x or y) by multiplying one or both equations by appropriate constants, so that when you add or subtract the equations, one of the variables cancels out.
Let's solve the system step by step:
1. Multiply the first equation by 6 and the second equation by 3 to make the coefficients of x in both equations the same:
6 * (3x) = 6 * (5y)
3 * (6x) - 3 * (7y) = 3 * (17)
Simplified, the equations become:
18x = 30y
18x - 21y = 51
2. Now, subtract equation 2 from equation 1 (equation 1 - equation 2) to eliminate the x variable:
(18x - 18x) - (30y - (-21y)) = (0) - (51)
0 + 51y = -51
Simplifying further:
51y = -51
3. Divide both sides of the equation by 51 to solve for y:
y = -51 / 51
y = -1
4. Now substitute this value of y back into either of the original equations (let's use the first one) to find the value of x:
3x = 5 * (-1)
3x = -5
x = -5 / 3
So, the solution to the system of equations is:
x = -5/3
y = -1