Answer:
The solution to this equation is x = 3 and y = -10.
Step-by-step explanation:
Our goal is to solve this equation by substitution. To do this, we must solve one equation for one variable in terms of the other variable and then plug this value into the other equation.
First, let's solve the first equation for y.
-x + y = -13
To do this, we should add x to both sides of the equation to isolate y on the left side.
y = x - 13
Now that we have this "value" for y, we can substitute this into the second equation.
3x - y = 19
3x - (x - 13) = 19
We should distribute the negative through the parentheses next.
3x - x + 13 = 19
Now we can combine like terms on the left side and subtract 13 from both sides to get the variable x alone on the left side of the equation.
2x = 6
Finally, we can solve for x by dividing both sides of the equation by 2.
x = 3
Now we can substitute this value for x back into either one of the original equations to solve for the variable y.
-x + y = - 13
-3 + y = -13
To solve, we simply add 3 to both sides of the equation.
y = -10
Therefore, the solution to this equation is x = 3 and y = -10. Remember that we can plug these values back into the original equations to check our answers.
Hope this helps!
