Final answer:
To solve the given system of linear equations, the elimination method is used, multiplying the first equation by 2, subtracting the second equation from it, and solving for y, then back-substituting to find x. The solution is x = -1 and y = 6.
Step-by-step explanation:
To solve the system of equations x + 2y = 11 and 2x - 3y = -20, you can use the method of substitution or elimination. In this case, let's use elimination.
- First, multiply the first equation by 2 to get a common coefficient for x: 2(x + 2y) = 2(11), which simplifies to 2x + 4y = 22.
- Now, we have a set of two new equations: 2x + 4y = 22 and 2x - 3y = -20.
- Subtract the second equation from the first: (2x + 4y) - (2x - 3y) = 22 - (-20). This gives us 7y = 42.
- Divide both sides by 7 to solve for y, yielding y = 6.
- Now substitute y back into one of the original equations to solve for x. Using the first equation: x + 2(6) = 11. Simplifying gives x + 12 = 11, and subtracting 12 from both sides gives x = -1.
The solution to the system of equations is x = -1 and y = 6.