Answer:
The answer is [tex]x=-\frac{50}{8}[/tex] and [tex]y=\frac{11}{2}.[/tex]
Step-by-step explanation:
Given:
-4x-2y=14
-10x+7y=-24
Now, to solve it by elimination:
[tex]-4x-2y=14[/tex] ......(1)
[tex]-10x+7y=-24[/tex] ......(2)
So, we multiply the equation (1) by 7 we get:
[tex]-28x-14y=98[/tex]
And, we multiply the equation (2) by 2 we get:
[tex]-20x+14y=-48[/tex]
Now, adding both the new equations:
[tex]-28x-14y+(-20x+14y)=98+(-48)[/tex]
[tex]-28x-14y-20x+14y=98-48[/tex]
[tex]-28x-20x-14y+14y=50[/tex]
[tex]-8x=50[/tex]
Dividing both the sides by -8 we get:
[tex]x=-\frac{50}{8}[/tex]
Now, putting the value of [tex]x[/tex] in equation (1):
[tex]-4x-2y=14[/tex]
[tex]-4(-\frac{50}{8})-2y=14[/tex]
[tex]\frac{200}{8} -2y=14[/tex]
[tex]25-2y=14[/tex]
Subtracting both sides by 25 we get:
[tex]-2y=-11[/tex]
Dividing both sides by -2 we get:
[tex]y=\frac{11}{2}[/tex]
Therefore, the answer is [tex]x=-\frac{50}{8}[/tex] and [tex]y=\frac{11}{2}.[/tex]
