Final answer:
This detailed answer provides a step-by-step guide to solving systems of linear equations using elimination. It explains the process of manipulating the equations to eliminate one variable, finding the remaining variable, and then substituting back in to find the other. The work is then checked by substituting the solution into the original equation.
Step-by-step explanation:
To solve these systems of linear equations using elimination and addition or subtraction, we need to eliminate one of the variables by manipulation.
4
Given that:
{ x + 3y = -14
{ 2x - 4y = 30
Multiply the first equation by 2 and the second by 1. We get:
{ 2x + 6y = -28
{ 2x - 4y = 30
Add the equations together:
2y = 2
y = 1
Substitute y = 1 into the first original equation we find that:
x = -17
The solution for this system is (x,y) = (-17,1)
5
Given that:
{ 4x - y = -5
{ -2x + 3y = 10}
...
6
Given that:
{ y - 3x = 11
{ 2y - x = 2}
...
Please complete each step in a similar fashion as I showed in the first example. Don't forget to check your work by substituting the solution into the original equation to ensure it holds true. This concept should help you with helping you understand the subtraction and addition method.
Learn more about Solving Systems of Linear Equations