Answer:
Step-by-step explanation:
(a)
Given the system of equation:
[tex]5x-2y=-6[/tex] .....[1]
[tex]2x-y=1[/tex] .....[2]
Multiply equation [2] by -2 we get;
[tex]-4x + 2y = -2[/tex] ......[3]
Add equation [1] and [3] to eliminate y and solve for x we have;
[tex]5x -2y+(-4x+2y) = -6-2[/tex]
[tex]5x -2y-4x+2y= -6-2[/tex]
Combine like terms;
[tex]x = -8[/tex]
Substitute the value of x in [2] we get;
2(-8)-y =1
-16-y = 1
Add 16 both sides we get;
-y = 17
or
y =-17
Answer; Solution for the given system of equation is (-8, -17)
Verify:
Substitute the value of x = -8 and y = -17 in the system of equation;
5x -2y = -6
5(-8)-2(-17) = -6
-40+34 = -6
-6 = -6 True
2x-y =1
2(-8)-(-17) = 1
-16+17 = 1
1 = 1 True.
(b)
Given the system of equation:
[tex]2x+3y=432[/tex] .....[1]
[tex]5x-2y=16[/tex] .....[2]
Multiply equation [2] by 3 and equation [1] by 2 we get;
[tex]15x -6y = 48[/tex] ......[3]
[tex]4x +6y = 864[/tex] ......[4]
Add equation [3] and [4] to eliminate y and solve for x we have;
[tex]15x -6y+4x+6y =48+864[/tex]
Combine like terms;
[tex]19x = 912[/tex]
Divide both sides by 19 we get
x = 48
Substitute the value of x in [2] we get;
5(48)-2y=16
240 -2y = 16
Subtract 240 from both sides we get;
-2y =-224
Divide both sides by -2 we get
y =112
Answer: Solution for the given system of equation is (48, 112)
Verify:
Substitute the value of x = 48 and y = 112 in the system of equation;
[tex]2x+3y=432[/tex]
[tex]2(48)+3(112)=432[/tex]
[tex]96+33+3y=432[/tex]
[tex]432=432[/tex] true
[tex]5x-2y=16[/tex]
[tex]5(48)-2(112)=16[/tex]
[tex]240-224=16[/tex]
16 = 16 true
