solve with addition:
-3x + y = 3
2x- 3y = 5
I would multiply the first by 3 and then add.
The y's will drop out
To solve the system of equations using addition, you need to eliminate one variable by adding the equations together. Here's how you can do it step by step:
1. Multiply both sides of the first equation by 3 to make the coefficients of "x" the same in both equations:
-3x + y = 3
Multiply both sides by 3:
(-3x + y) * 3 = 3 * 3
-9x + 3y = 9
2. Multiply both sides of the second equation by 5 to make the coefficients of "x" the same in both equations:
2x - 3y = 5
Multiply both sides by 5:
(2x - 3y) * 5 = 5 * 5
10x - 15y = 25
3. Now, you have two equations with the same coefficient for "x":
-9x + 3y = 9
10x - 15y = 25
4. Add the two equations together to eliminate "x":
(-9x + 3y) + (10x - 15y) = 9 + 25
-9x + 10x + 3y - 15y = 34
x - 12y = 34
5. Now you have a new equation: x - 12y = 34
At this point, you have eliminated the variable "x" and obtained a single equation in terms of "y". Let's proceed to solve for "y":
6. Multiply both sides of the first equation by 12 to eliminate the coefficient of "x":
x - 12y = 34
Multiply both sides by 12:
(x - 12y) * 12 = 34 * 12
12x - 144y = 408
7. Now, you have two equations with the same coefficient for "x":
x - 12y = 34
12x - 144y = 408
8. Add the two equations together to eliminate "x":
(x - 12y) + (12x - 144y) = 34 + 408
x + 12x - 12y - 144y = 442
13x - 156y = 442
9. Now, you have a new equation: 13x - 156y = 442
At this point, you have eliminated the variable "y" and obtained a single equation in terms of "x". Let's solve for "x":
10. Solve the equation 13x - 156y = 442 for "x":
13x - 156y = 442
13x = 442 + 156y
x = (442 + 156y) / 13
Now you have the solution for "x" in terms of "y".