There are several methods to solve a linear system, but one common way is to use substitution. Here's how it works:
1. Solve one of the equations for one variable in terms of the other. For example, from the first equation x+y=1, we can isolate y by subtracting x from both sides: y=1-x.
2. Substitute the expression for that variable into the other equation. Using the second equation 2x-3y=-18, we can replace y with 1-x: 2x-3(1-x)=-18.
3. Simplify and solve for the remaining variable. Distribute the -3: 2x-3+3x=-18, which simplifies to 5x=-15. Divide both sides by 5: x=-3.
4. Use the value(s) found in (3) to find the other variable(s). We can use either equation, but let's use the first one. If x=-3, then y=1-(-3)=4.
Therefore, the solution to the linear system x+y=1, 2x-3y=-18 is x=-3 and y=4.
What is the solution to the linear system x+y=1, 2x-3y=-18
1 answer
1 answer