The solution to the system is (8, -12).
Step-by-step explanation:
Given equations are;
1/4x-1/2y=8 Eqn 1
1/2x+3/4y=-5 Eqn 2
Multiplying both equations by 4
[tex]4(\frac{1}{4}x-\frac{1}{2}y=8),\ \ \ \ 4(\frac{1}{2}x+\frac{3}{4}y=-5)\\4*\frac{1}{4}x-\frac{1}{2}y*4=8*4, \ \ \ \ 4*\frac{1}{2}x+\frac{3}{4}y*4=-5*4\\x-2y=32 \ \ \ Eqn \ 3\ , \ \ \ \ 2x+3y=-20\ \ \ \ Eqn\ 4[/tex]
Multiplying Eqn 3 by -2
[tex]-2(x-2y=32)\\-2x+4y=-64\ \ \ \ Eqn\ 5[/tex]
Adding Eqn 4 and Eqn 5
[tex](2x+3y)+(-2x+4y)=-20+(-64)\\2x+3y-2x+4y=-20-64\\7y=-84[/tex]
Dividing both sides by 7
[tex]\frac{7y}{7}=\frac{-84}{7}\\y=-12[/tex]
Putting y=-12 in Eqn 3
[tex]x-2(-12)=32\\x+24=32\\x=32-24\\x=8[/tex]
The solution to the system is (8, -12).
Keywords: linear equations, addition
Learn more about linear equations at:
- brainly.com/question/1648434
- brainly.com/question/1648978
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