Final answer:
The solution to the system of equations 2x - 3y = -13 and 4x + 2y = 6 is found by using the elimination method to first solve for x, getting x = -0.5, and then substituting this value into one of the original equations to solve for y, which results in y = 4.
Step-by-step explanation:
To find the values of x and y that satisfy the system of equations:
First, we can use the method of substitution or elimination. Let's use elimination in this case. Multiply the second equation by 1.5 to make the coefficients of y equal with opposite signs:
- (4x + 2y) × 1.5 = 6 × 1.5
- 6x + 3y = 9
Add this to the first equation:
- 2x - 3y = -13
- +
- 6x + 3y = 9
- ---------
- 8x = -4
Divide by 8 to get x = -0.5.
To find y, substitute x into the second original equation:
- 4(-0.5) + 2y = 6
- -2 + 2y = 6
- 2y = 8
- y = 4
So, the solution to the system of equations is x = -0.5 and y = 4.