1.Solve the system of equations using the Addition method. 2a + 3b = -13a + 5b = -2?

5)(4,5)

2a + 3b = -2 -13a + 5b = -2 multipy the 1st via 5 and the 2nd via (-3) 5(2a + 3b) = 5(-2) -3(-13a + 5b) = -3(-2) Now upload 10a + 15b = -10 39a - 15b = 6 ---------------------- 49a /// /// = -4 49a = -4 a = -4/40 9 2a+3b = -2 b = (-2-2a)/3 b = (-2+8/40 9)/3 b = -ninety/40 9 *one million/3 b = -30/40 9;

1)
2a + 3b = -13
a + 5b = -2

2a + 3b = -13
3b = -13 - 2a
b = (-13 - 2a)/3
5b = 5(-13 - 2a)/3

a + 5b = -2
a + 5(-13 - 2a)/3 = -2
3[a + (-65 - 10a)/3] = 3(-2)
3a - 65 - 10a = -6
3a - 10a = -6 + 65
-7a = 59
a = -59/7

2a + 3b = -13
-118/7 + 3b = -13
3b = -13 + 118/7
3b = 27/7
b = (27/7)/3
b = 27/21
b = 9/7

∴ a = -59/7 , b = 9/7

= = = = = = = =

2)
x + y = 10
x - y = 8

x + y = 10
y = 10 - x

x - y = 8
x - (10 - x) = 8
x - 10 + x = 8
x + x = 8 + 10
2x = 18
x = 18/2
x = 9

x + y = 10
9 + y = 10
y = 10 - 9
y = 1

∴ x = 9 , y = 1
(answer c)

= = = = = = = =

3)
3x - y = 9
2x + y = 6

3x - y = 9
y = 3x - 9

2x + y = 6
2x + (3x - 9) = 6
2x + 3x - 9 = 6
5x = 6 + 9
5x = 15
x = 15/5
x = 3

3x - y = 9
3(3) - y = 9
9 - y = 9
y = 9 - 9
y = 0

∴ x = 3 , y = 0
(answer a)

= = = = = = = =

4)
x + y = -7
3x + y = -9

x + y = -7
y = -7 - x

3x + y = -9
3x + (-7 - x) = -9
3x - 7 - x = -9
3x - x = -9 + 7
2x = -2
x = -2/2
x = -1

x + y = -7
-1 + y = -7
y = -7 + 1
y = -6

∴ x = -1 , y = -6
(answer d)

= = = = = = = =

5)
x + 3y = 19
3y = 19 - x
y = (19 - x)/3

x - y = -1
x - (19 - x)/3 = -1
3[x - (19 - x)/3] = 3(-1)
3x - 19 + x = -3
3x + x = -3 + 19
4x = 16
x = 16/4
x = 4

x + 3y = 19
4 + 3y = 19
3y = 19 - 4
3y = 15
y = 15/3
y = 5

∴ x = 4 , y = 5
(answer c)

1.
2a+3b= -13
a+5b =-2
multiply equation (2) by 2 and subtract from (1)
2a+10b=-4
-7b=-9
b=9/7
a+5b=-2
a+5(9/7)=-2
a=-2-45/7
a=-59/7