Respuesta :
Part a: -2 is used to eliminate the x-terms when adding with the second equation.
Part b: [tex]-\frac{1}{2}[/tex] is used to eliminate the x-terms when adding with the second equation.
Part c: [tex]\frac{1}{2}[/tex] is used to eliminate the x-terms when adding with the second equation.
Part d: 2 is used to eliminate the x-terms when adding with the second equation.
Explanation:
Part a: The equations are [tex]3 x-8 y=1[/tex] and [tex]6 x+5 y=12[/tex]
To eliminate the x-terms from both the equations, let us multiply -2 with the first equation and hence it becomes [tex]-6x+16y=-2[/tex]
Adding the two equation, we get,
[tex]-6x+16y+6 x+5 y=-2+12[/tex]
Simplifying, we get,
[tex]21y=10[/tex]
Thus, the x-terms are eliminated when adding the equations.
Hence,-2 is used to eliminate the x-terms when adding with the second equation.
Part b: The equations are [tex]-8 x+10 y=16[/tex] and [tex]-4 x-5 y=13[/tex]
To eliminate the x-terms from both the equations, let us multiply [tex]-\frac{1}{2}[/tex] with the first equation and hence it becomes [tex]4 x-5 y=-8[/tex]
Adding the two equation, we get,
[tex]4x-5y-4x-5y=-8+13[/tex]
Simplifying, we get,
[tex]0=5[/tex]
Thus, the x-terms are eliminated when adding the equations.
Hence, [tex]-\frac{1}{2}[/tex] is used to eliminate the x-terms when adding with the second equation.
Part c: The equations are [tex]10 x-4 y=-8[/tex] and [tex]-5 x+6 y=10[/tex]
To eliminate the x-terms from both the equations, let us multiply [tex]\frac{1}{2}[/tex] with the first equation and hence it becomes [tex]5x-2y=-4[/tex]
Adding the two equation, we get,
[tex]5x-2y-5x+6y=-4+10[/tex]
Simplifying, we get,
[tex]4y=6[/tex]
Thus, the x-terms are eliminated when adding the equations.
Hence, [tex]\frac{1}{2}[/tex] is used to eliminate the x-terms when adding with the second equation.
Part d: The equations are [tex]-2 x+6 y=3[/tex] and [tex]4 x+3 y=9[/tex]
To eliminate the x-terms from both the equations, let us multiply 2 with the first equation and hence it becomes [tex]-4x+12y=6[/tex]
Adding the two equation, we get,
[tex]-4x+12y+4x+3y=6+9[/tex]
Simplifying, we get,
[tex]15y=15[/tex]
Thus, the x-terms are eliminated when adding the equations.
Hence, 2 is used to eliminate the x-terms when adding with the second equation.
Answer:
1. 10x-4y=-8 matches: 1/2
-5x+6=10
2. -2x+6y=3 matches: 2
4x+3y=9
3. 3x-8y=1 matches: -2
6x+5y=12
4. -8x+10y=16 matches: -1/2
-4x-5y=13
