pleae help solve: 3x-5y=7 and 5x-2y=-1
3x-5y=7 times 5 15x-25y=35
5x-2y=-1times 3 15x -6y=-3
subtract second from first
0x -19y = 38
y = -2
3x-5(-2) = 7
3x +10 =7
3x = -3
x = -1
check
3(-1) -5(-2) = 7 yes
5(-1)-2(-2)=-1 yes
25y to the second power times x to the second power plus 20xy to the second power plus 4x to the second power
To solve the system of equations 3x - 5y = 7 and 5x - 2y = -1, we can use either the substitution method or the elimination method. Let's use the elimination method.
Step 1: Multiply the first equation by 2, and the second equation by 5 to make the coefficients of 'y' in both equations equal:
2 * (3x - 5y) = 2 * 7
5 * (5x - 2y) = 5 * (-1)
Simplifying these equations, we get:
6x - 10y = 14
25x - 10y = -5
Step 2: Now subtract the first equation from the second equation to eliminate the variable 'y':
(25x - 10y) - (6x - 10y) = -5 - 14
Simplifying, we get:
25x - 10y - 6x + 10y = -19
Now, the 'y' terms, -10y and +10y, cancel out, leaving us with:
25x - 6x = -19
Step 3: Combine like terms on the left side of the equation:
19x = -19
Step 4: Divide both sides of the equation by 19 to solve for 'x':
x = -19 / 19
Simplifying, we get:
x = -1
Step 5: Substitute the value of 'x' (-1) into either of the original equations to solve for 'y'. Let's use the first equation:
3x - 5y = 7
Plugging in x = -1:
3(-1) - 5y = 7
Simplifying, we get:
-3 - 5y = 7
Step 6: Now, isolate 'y' by adding 3 to both sides of the equation:
-5y = 7 + 3
-5y = 10
Step 7: Divide both sides of the equation by -5 to solve for 'y':
y = 10 / -5
Simplifying, we get:
y = -2
Therefore, the solution to the system of equations 3x - 5y = 7 and 5x - 2y = -1 is x = -1 and y = -2.