Answer:
1. x = 1, y = 2.
12. x = 1, y = -3.
Explanation:
I won't do all these for you, just the first and the last. The method is similar for all 12.
1.
y = x + 1
x + y = 3
Substitute y = x + 1 into the second equation:
x + y = 3 so:
x + (x + 1) = 3
2x + 1 = 3
2x + 1 -1 = 3 - 1
2x = 2
x = 1.
Now substitute x = 1 into the first equation to get the value of y:
y = x + 1
y = 1 + 1
y = 2.
12.
4x = y + 7
3x + 4y + 9 = 0
Solve for y in the first equation:
4x = y + 7 Subtract 7 from both sides of the equation:
4x - 7 = y + 7 - 7
y = 4x - 7.
Now substitute y = 4x - 7 in the second equation:
3x + 4y + 9 = 0 so:
3x + 4(4x - 7) + 9 = 0
3x + 16x - 28 + 9 = 0
19x - 19 = 0
19x - 19 + 19 = 0 + 19
19x = 19
x = 19/19 = 1.
Now substitute x = 1 in the first equation:
4x = y + 7
4*1 = y + 7 Subtract 7 from both sides of the equation:
4 - 7 = y + 7 - 7
-3 = y.