Answer:
The solution to the system of equations be:
x = 0.5, y = -0.5
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}2x+4y=1\\ 3x-5y=7\end{bmatrix}[/tex]
Multiply 2x+4y=1 by 3: 6x+12y=3
Multiply 3x-5y=7 by 2: 6x-10y=14
[tex]\begin{bmatrix}6x+12y=3\\ 6x-10y=14\end{bmatrix}[/tex]
subtracting the equations
[tex]6x-10y=14[/tex]
[tex]-[/tex]
[tex]\underline{6x+12y=3}[/tex]
[tex]-22y=11[/tex]
solve -22y for y
[tex]-22y=11[/tex]
Divide both sides by -22
[tex]\frac{-22y}{-22}=\frac{11}{-22}[/tex]
Simplify
[tex]y=-\frac{1}{2}[/tex]
[tex]y = -0.5[/tex]
For 6x+12y=3 plug in y = -1/2
[tex]6x+12\left(-\frac{1}{2}\right)=3[/tex]
[tex]6x-12\cdot \frac{1}{2}=3[/tex]
[tex]6x-6=3[/tex]
Add 6 to both sides
[tex]6x-6+6=3+6[/tex]
[tex]\frac{6x}{6}=\frac{9}{6}[/tex]
Simplification
[tex]x=\frac{3}{2}[/tex]
[tex]x = 1.5[/tex]
Therefore, the solution to the system of equations be:
x = 0.5, y = -0.5
