Question

Soo-Jin began solving the system (x+y=22) and (2x-5y=-10) as shown. She made a mistake. In what line does the mistake occur?

a) Solving (x+y=22)

b) Setting up the system of equations

c) Solving (2x-5y=-10)

d) Combining the two equations

Answer 1

The mistake occurs in line d) Combining the two equations. To solve the system of equations correctly, you need to solve one equation for one variable and then substitute that value into the other equation.

Step-by-step explanation:

The mistake occurs in line d) Combining the two equations.

Let's go through the steps to solve the system of equations correctly:

1. Solve (x+y=22) for y. Subtract x from both sides to get y = 22 - x.
2. Substitute this value of y into the second equation (2x-5y=-10).
3. Replace y with (22 - x) in the second equation and solve for x: 2x - 5(22 - x) = -10.
4. Simplify and solve for x.
5. Once you have the value of x, substitute it back into the first equation to find y.

If the mistake occurred in line d), then the error would most likely be in incorrectly distributing the negative sign when substituting y into the second equation. Double-check the distribution of the negative sign to find the error.