Answer:
Question b
[tex]\textsf{Equation 1:} \ \dfrac12x-2y=-13[/tex]
[tex]\textsf{Equation 2:} \ x-4y=8[/tex]
Multiply Equation 2 by two:
[tex]\implies \textsf{Equation 3:} \ x+4y=-26[/tex]
Subtract Equation 2 from Equation 3:
[tex]\begin{aligned}x-4y & =8\\- \ \ \ x+4y & =-26\\\cline{1-2}-8y & =34\end{aligned}[/tex]
Solve for y:
[tex]\implies -8y=34[/tex]
[tex]\implies y = -\dfrac{17}{4}[/tex]
Substitute found value of y into Equation 2 and solve for x:
[tex]\implies x-4\left(-\dfrac{17}{4}\right)=8[/tex]
[tex]\implies x+17=8[/tex]
[tex]\implies x=-9[/tex]
Question a
[tex]\textsf{Equation 1:} \ x+y=2[/tex]
[tex]\textsf{Equation 2:} \ -3x-y=5[/tex]
Add Equation 1 and Equation 2:
[tex]\begin{aligned}x+y & = 2\\+ \ \ \ -3x-y & =5\\\cline{1-2}-2x & = 7\end{aligned}[/tex]
Solve for x:
[tex]\implies -2x=7[/tex]
[tex]\implies x = -\dfrac{7}{2}[/tex]
Substitute found value of x into Equation 1 and solve for y:
[tex]\implies \left(-\dfrac{7}{2}\right)+y=2[/tex]
[tex]\implies y=\dfrac{11}{2}[/tex]
