1) 14x-2y=46
-7x+y=-23
-7x+y=-23
Using the 2nd equation, y = -23+7x
Substitute this into the 1st equation for y
14x - 2(-23+7x) = 46
14x + 46 -14x = 46
46=46
Therefore there are multiple solutions.
Note that the 1st equation is the second equation times -2
2) 5x+ y =8
-3x +2y = -10
This time let's start with the 1st equation.
y = 8-5x and substitute this into the 2nd equation
-3x + 2(8-5x) = -10
-3x + 16 - 10x = -10
-13x = -26
x = 2
Now use x=2 and evaluate either of the equations for y
5(2) + y = 8
10+y = 8
y = -2
Solution (2,-2)
Solve by elimination
3) -15x + 9y=27
-5x - y = 17
Solve by elimination
3) -15x + 9y=27
-5x - y = 17
We need to eliminate one of the variables so let's multiply the 2nd equation by -3. This give us
-15x + 9y = 27
15x + 3y = -51
Add the equations together
12y = -24
y = -2
Use y=-2 and solve for x
-5x +2 = 17
-5x = 15
x = -3
Solution (-3,-2)
4) -7x - 8y =-23
4x + 4y =12
Multiply the 2nd equation by 2
-7x - 8y = -23
8x + 8y = 24
Adding the two equations together we have
x = 1
And solving for y
4(1) + 4y = 12
4y = 8
y = 2
Soltuion (1,2)
