Solving Linear equations - Sudstitution (Algebra)?

Question

Find the common sulution for each system of equations . Check each solution.


1) 2x + y = 4 2x + 3 = 0 _________
2) 2x + y + 0 x - y = 1 _________
3) 3x + 4y = -11 7x - 5y = 3 _________
4) 2x + y = -1 -2x + y = 3 _________
5) 3x - 5y = 4 4x + 3y = 15________
6) 3x - 2y = 5 -4y + 3y = 1________
7) 3x -4y = 5 5x + 4y = 3 ________
8) 4x = 3y - 10 2y = 22 - 5x________
9) 2x + 6y = 14 3x - 4y = -5________
10) 1/2y = 2 - 2x 6x = y + 1 _________

Answer 1

Here are a couple to get you started.

1. 2x +y = 4
2x + 3 = 0

You can solve the second equation for x.
2x+3 = 0
Subtract 3 from each side.
2x = -3
Divide both sides by 2
x = -3/2

Now plug this into the first equation.
2(-3/2) + y = 4
-3 + y = 4
y = 7
Answer: (-3/2, 7)
To check simplify, plug x = -3/2 and y = 7 into each equation to see if it is true.
For example,
2(-3/2) + 7 = 4
-3 + 7 = 4
4 = 4

2(-3/2) + 3 = 0
-3+3 = 0
0 = 0
Both equations are true, so (-3/2,7) must be the solution.

2. 2x+y = 0
x-y = 1

You can solve the first equation for y by subtracting 2x from each side.
y = -2x
Plug this into the second equation.
x - (-2x) = 1
x + 2x = 1
3x = 1
x = 1/3

Now go back to the equation where you solved for y.
y = -2x
Plug in the y value you just found.
y = -2(1/3)
y = -2/3

Answer: (1/3, -2/3)

Check:
2(1/3) + -2/3 = 0
2/3 - 2/3 = 0
0 = 0

1/3 - (-2/3) = 1
1/2 + 2/3 = 1
1 = 1
Both equations are true, so I know my solution is correct.

Now you try the others.

Answer 2

question a million [3 a million 21] [a million a million a million] multilpy this by utilising -a million and remedy [3 a million 21] [-a million -a million -a million ] upload the two equations [2 0 20] this suggests x = 10 plug into equation 2 10(x) - y = a million y = 9 question 2 utilising the comparable approach the respond comes out to x = 2 y = 3