Solve this system by addition. -3x-7y=-10 and x+3y=4?

Question

The actual way this looks is this in case this helps:

-3x-7y=-10
x+3y=4

Answer 1

Multiply the bottom by 3 and add it to the first:
-3x - 7y = -10
3x + 9y = 12
2y = 2
y = 1

Then plug this back into either equation to get x
x + 3(1) = 4
x + 3 = 4
x =1

So x = 1 and y = 1

Answer 2

x=1
y=1

Answer 3

3. remedy the following equipment of equations, making use of the eliminating approach: 3x - 4y = -30 7x + 4y = 10 3x - 4y = -30 3x = -30 + 4y 3x + 30 = 4y 3/4x + 30/4 = y 7x + 4y = 10 4y = 10 - 7x y = 10/4 - 7/4x y-y = 0 (3/4x + 30/4) - (10/4 - 7/4x) = 0 3/4x + 30/4 - 10/4 + 7/4x = 0 10/4x + 20/4 = 0 10/4x = -20/4 10x = -20 x = -2 6. remedy the following equipment of equations, making use of the graphing approach: 3x - 2y = 5 2x + 5y = -3 3x - 2y = 5 -2y = 5 - 3x y = -5/2 + 3/2x 2x + 5y = -3 5y = -3 - 2x y = -3/5 - 2/5x y = y -5/2 + 3/2x = -3/5 - 2/5x 3/2x + 2/5x = -3/5 + 5/2 15/10 x + 4/10x = -6/10 + 25/10 19/10x = 19/10 19x = 19 x = a million 10. remedy the following equipment of equations, making use of the substitution approach: 4x - 3y = 33 x = - 4y - 25 4x - 3y = 33 -3y = 33 - 4x y = -33/3 + 4/3x y = -11 + 4/3x x = - 4y - 25 replace y by -11 + 4/3x x = -4 (-11 + 4/3x) - 25 x = forty 4 - 16/3x - 25 x + 16/3x = 19 3/3x + 16/3x = 19 19/3x = 19 a million/3x = a million x = 3 similar for different issues

Answer 4

x=1, y=1

Answer 5

Well you can do it by matrices which is equivalent to:

-3x-7y=-10
3x+9y=12
2y=2
y=1
x=1

or
| -3 -7 | -10 |
| 1 3 | 4 |

=

| -3 -7 | -10 |
| 3 9 | 12 |

=

| -3 -7 | -10 |
| 0 2 | 2 |

=

| -3 -7 | -10 |
| 0 1 | 1 |

=
| -3 -7 | -10 |
| 0 7 | 7 |

=

| -3 0 | -3 |
| 0 1 | 1 |

=

|1 0 | 1 |
| 0 1 | 1|

Which is the same.

Answer 6

3x+7y=10 is the same as -3x-7y=-10
x= 4-3y
3(4-3y)+7y=10
12-9y+7y=10
-9y+7y=10-12
-2y=-2
y=1
x=4-3y
x=4-3(1)
x=4-3
x=1

Answer 7

just go down, and add all like terms
-3x + x =-2x
-7y + 3y = -4y
-10 + 4 = -6

then put all the answers in order: -2x - 4y = -6

Answer 8

A = [-3, -7; 1, 3]
B = [-10 ; 4]
X = [x; y]

AX = B

X = inverse(A) * B

inverse(A) = [3, 7; -1, -3]/(-3*3 + 7*1)
=[-3/2, -7/2; 1/2, 3/2]

X = [15-14; -5+6] = [1; 1]

Answer 9

-3*x-7*y=-10
x+3*y=4

multiplying the second equation with 3;
-3*x-7*y=-10
3*x+9*y=12

subtracting 2 equations;

2*y=2----------->y=1

putting y=1 in one of the eqautions---->x=1. QED

Answer 10

-3x -7y = -10 ---- (i)
x + 3y = 4 ----(ii)

multiplying (ii) by 3 we get

3x + 9y = 12 ----(iii)

adding (i) and (iii)

-3x -7y = -10 ---- (i)
3x + 9y = 12 ----(iii)

we get

2y = 2
=> y=1 ----(iv)

putting the value of y=1 in (i), (ii) or (iii) we get

x=1