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Solve the simultaneous equations
2x + 4y = 1
3x - 5y = 7
y=1.5 x=
What does x equal

Sagot :

absor201

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

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