Answer:
1) we get value of x = -4 and y = -4
2) we get value of x = -7 and y = 3
Step-by-step explanation:
1) Identify the solution to the system of equations.
[tex]y=\frac{3}{2}x+2\:and\:y=\frac{1}{4}x-3[/tex]
Looking at the graph we can see that two points intersect at (-4,-4) so it is the solution of the system of equations. Verifying by solving:
Let:
[tex]y=\frac{3}{2}x+2--eq(1)\\y=\frac{1}{4}x-3--eq(2)[/tex]
Put value of y from eq(1) into eq(2)
[tex]\frac{1}{4}x-3=\frac{3}{2}x+2\\\frac{x-12}{4}=\frac{3x+4}{2} \\2(x-12)=4(3x+4)\\2x-24=12x+16\\2x-12x=16+24\\-10x=40\\x=40/-10\\x=-4[/tex]
Now put value of x in eq(2)
[tex]y=\frac{1}{4}x-3\\y=\frac{1}{4}(-4)-3\\y=-1-3\\y=-4[/tex]
So, we get x = -4 and y = -4
2)
[tex]9x+14y=-21\\-x+7y=28[/tex]
Let: [tex]9x+14y=-21--eq(1)\\-x+7y=28--eq(2)[/tex]
Multiply eq(2) with 9 and add both equations
[tex]9x+14y=-21\\-9x+63y=252\\------\\77y=231\\y=231/77\\y=3[/tex]
Put value of y in eq(2)
[tex]-x+7y=28\\-x+7(3)=28\\-x+21=28\\-x=28-21\\-x=7\\x=-7[/tex]
So, value of x = -7 and y = 3
