a. 3x - 2y = 14
-2x + 2y = -10 just add the equations and we have :
x = 4 to find y......just substitute for x in either of the equations
3(4) - 2y = 14
12 - 2y =14 subtract 12 from both sides
-2y = 2 divide both sides by -2
y = -1
So......the solution is : (x, y) = ( 4, -1)
b. y = 5x + 3
-2x - 4y = 10
Substitute the first equation for y into the second equation
-2x - 4[5x + 3] = 10 simplify
-2x - 20x - 12 = 10
-22x - 12 = 10 add 12 to both sides
-22x = 22 divide both sides by -22
x = -1
And using y = 5x + 3, we have that
y = 5(-1) + 3 = -2
So........the solution is (x, y) = ( -1, -2)
(a) 3x - 2y = 14 ------(1)
-2x +2y = -10 ------ (2)
(1) + (2)
x = 4 ------(3)
Subst. (3) into (1)
3(4) - 2y = 14
3(4) - 14 = 2y
-2 = 2y
y = -1
Therefore x=4 and y= -1.
And I believe that is what your teacher will advise you to do.(Method of Elimination)
(b) y = 5x+3 ------(1)
-2x - 4y = 10 ------- (2)
Let's make (2) less complicated.
2x + 4y = -10
x + 2y = -5 ------ (3)
Looks better.
Your teacher may want you to do Method of Substitution......
so
Subst. (1) into (3),
x + 2(5x+3) = -5
x+10x+6 = -5
11x = -11
x = -1 ------ (4)
Subst (4) into (1)
y = 5(-1) + 3 = -5 +3 = -2
Therefore x=-1 and y=-2