Question

4x + 5y = 22
7x - 3y = -32

Answer 1

To solve the system of equations 4x + 5y = 22 and 7x - 3y = -32, you can use the method of substitution. The solution is x = 8/7 and y = 108/7.

Step-by-step explanation:

To solve the system of equations 4x + 5y = 22 and 7x - 3y = -32, we can use the method of substitution. We'll solve one equation for one variable and substitute it into the other equation.

1. Solve the first equation for x: 4x = 22 - 5y ⟹ x = (22 - 5y)/4
2. Substitute x into the second equation: 7((22 - 5y)/4) - 3y = -32
3. Simplify and solve for y: 22 - (35/4)y - 3y = -32 ⟹ 22 - (35/4 + 12/4)y = -32 ⟹ (35/4 + 12/4)y = 54 ⟹ (14/4)y = 54 ⟹ y = 216/14 = 108/7
4. Substitute y back into the expression for x: x = (22 - 5(108/7))/4 = 8/7

Therefore, the solution to the system of equations is x = 8/7 and y = 108/7.

Answer 2

x = -2

y = 6

Step-by-step explanation:

i multiplied the 1st equation by 3 and the 2nd by 5 to get the y-terms to zero out

12x + 15y = 66

+ 35x - 15y = -160

47x = -94

x = -94/47

x = -2

substitute -2 for 'x' to solve for 'y':

4(-2) + 5y = 22

-8 + 5y = 22

5y = 30

y = 6