Please show me step by step on how to solve elimination of system of equations.(3x+2y=7, y=-3x+11)?

(3x+2y=7, y=-3x+11)
substitue y=-3x+11 to te first equation 3x+2y=7
3x+2(-3x+11)=7
3x-6x+22=7
-3x=-15
x=5
solve for y
y=-3(5)+11=-4

There are countless trouble-free techniques to unravel this form of problem. i visit describe the least puzzling for this problem and clarify why? a million) look on the coefficients for the two variables in the two equations. If any of the coefficients is a a million, then it may be least puzzling to apply the substitution technique. 2) resolve for the variable that has a coefficient of a million so 4x - y = 20 turns into 4x - 20 = y 3) subsequent exchange the "value" that y is comparable to into the different eq'n. 3x - 4(4x-20)= 2 4) resolve for x 3x - 16x +80 = 2 -13x= -seventy 8 x = 6 5) Now take that value and exchange for x in any of the three equations that have an x and y. choosing the consequence from step 2 turns into 4(6) -20 = y 4 = y 6) Now examine for high quality artwork. exchange 6 for x and four for y into the two eq'ns. 3(6) - 4( 4) = 2 actual 4(6) - 4 = 20 actual on the grounds that the two statements are actual the artwork is right. hence the respond is the main appropriate value. Write the final answer as a coordinate pair (6,4).

3x + 2y = 7
3x + y = 11

3x + 2y = 7
- 3x - y = - 11-----ADD

y = - 4

3x - 4 = 11
3x = 15
x = 5

x = 5 , y = - 4

3x + 2y = 7
y = -3x + 11

y = -3x + 11
3x + y = 11

...3x + 2y = 7
-- 3x + y = 11 (subtraction)
---------------------
y = -4

3x + 2y = 7
3x + 2(-4) = 7
3x + (-8) = 7
3x - 8 = 7
3x = 7 + 8
3x = 15
x = 15/3
x = 5

∴ x = 5 , y = -4

To solve by elimination (even though you have it in the perfect form for substitution), you want to keep both variables on the same side in both equations, so we rearrange the second equation to give

3x + 2y = 7
3x + y = 11 <---- (This is the rearranged one)

OK, so the important thing to realise here is that, in each equation, one side of the equation is equal to the other. They are both the same, and completely interchangeable. We can do whatever we like, so long as we keep them the same, by performing the same operations on both sides at the same time.

To solve by elimination, we want to subtract left side of the second equation from the left side of the first equation. At the same time, we also have to subtract the same number from the other side of the first equation as well to keep the equality. Instead of subtracting "3x + y" from the right side of the first equation, we can subtract 11. Why? Because 11 is the same as 3x + y! So we now have one equation:

3x + 2y - (3x + y) = 7 - 11
3x + 2y - 3x - y = -4
0x + y = -4
y = -4

Now we have the value of y, we can work out x by substituting -4 into an equation instead of y (since we now know that they are the same).

3x + 2y = 7
3x + 2(-4) = 7
3x - 8 = 7
3x = 15
x = 5

So now you have solved the system. It has one solution: x = 5, y = -4.

3x + 2y = 7_____(1)
y = -3x + 11_____(2)
substitute equation (2) into equation (1);
3x + 2(-3x + 11) = 7
3x - 6x + 22 = 7
-3x = -15
x = 5

substitute x = 5 into equation (2);
y = -3(5) + 11
y = -15 + 11
y = -4