10x-5y=20
7x-5y=-26
Eq1: 10x-5y = 20.
Eq2: 7x-5y = -26.
Multiply Eq1 by -1:
-10x+5y = -20,
+7x-5y = -26.
Sum:x = -3x+0 = -46,
x = -46/-3 = 15 1/3.
In Eq2, substitute 46/3 for x:
7(46/3) - 5y = -26,
Solve for y and get:
26 2/3 = 80/3.
Solution Set = (x,y) = (15 1/3,26 2/3).
Check the given Eqs and make sure the signs are correct.
To solve this system of equations, we can use the method of elimination. The first step is to eliminate one variable from the equations by adding or subtracting the equations so that the coefficients of one of the variables become the same.
In this case, we can eliminate the variable "y" by multiplying the first equation by 7 and the second equation by 10:
Equation 1: 7(10x - 5y) = 7(20) -> 70x - 35y = 140
Equation 2: 10(7x - 5y) = 10(-26) -> 70x - 50y = -260
Now we have two equations:
70x - 35y = 140
70x - 50y = -260
To eliminate the variable "x," we can subtract the second equation from the first equation:
(70x - 35y) - (70x - 50y) = 140 - (-260)
70x - 35y - 70x + 50y = 140 + 260
15y = 400
Now we have a simplified equation with just one variable:
15y = 400
To isolate "y," divide both sides of the equation by 15:
y = 400 / 15
Simplifying the right side:
y = 26.67
Now that we have the value of "y," we can substitute it back into one of the original equations to solve for "x." Let's use the first equation:
10x - 5(26.67) = 20
10x - 133.35 = 20
10x = 20 + 133.35
10x = 153.35
Divide both sides by 10:
x = 153.35 / 10
Simplifying the right side:
x = 15.34
Therefore, the solution to the system of equations is x = 15.34 and y = 26.67.