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Linear Systems of Equations in Two Variables (Grade 10)

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Linear Systems of Equations in Two Variables

1. 
Select the solution to the following linear system.
[math]-5x-3y-9 = 0[/math]
[math]4x-18y-54=0[/math]
  1. [math]x=-3, y=0[/math]
  2. [math]x=0, y =-3[/math]
  3. [math]x=3, y=0[/math]
  4. [math]x=0, y=3[/math]
2. 
Which linear system has the solution [math]x=-2[/math] and [math]y=6[/math]?
  1. [math]x+3y=16; \ \ \ 4x+4y=16[/math]
  2. [math]x+2y=-2; \ \ \ 2x+4y=-4[/math]
  3. [math]x+3y=17; \ \ \ 2x+y=15[/math]
  4. [math]2x+y=-2; \ \ \ x+y=16[/math]
3. 
Select the solution to the following linear system.
[math]-6y+11x=-36[/math]
[math]-4y+7x=-24[/math]
  1. [math]y=0, x=-6[/math]
  2. [math]y=6, x=0[/math]
  3. [math]y=0, x=6[/math]
  4. [math]y=-6, x=0[/math]
4. 
Solve for [math]y[/math] in the following system of equations.
[math]x-y=-1[/math]
[math]3x+5y=21[/math]
  1. 2
  2. 9
  3. 3
  4. 12
5. 
Solve for [math]x[/math] in the following system of equations.
[math]14x+5y=31[/math]
[math]2x-3y=-29[/math]
  1. 9
  2. 1
  3. -9
  4. -1
6. 
The first equation of a linear system is: [math]2x+3y=52.[/math] Choose a second equation to form a linear system with infinite solutions:
(i)[math]2x+3y=-260[/math]; (ii)[math]-10x-15y=-260[/math]; (iii)[math]-10x+3y=-260[/math]; (iv)[math]-10x+3y=255[/math]
  1. Equation (iii)
  2. Equation (iv)
  3. Equation (i)
  4. Equation (ii)
7. 
Solve for [math]y[/math].
[math]y=-(13/4)x+7[/math]
[math]y=(3/4)x-9[/math]
  1. 4
  2. 6
  3. -4
  4. -6
8. 
Create a linear system to model this situation: A man is 3 times as old as his daughter. In 13 years, he will be 2 times as old as his daughter will be.
  1. [math]m=d+3; m+13=2d[/math]
  2. [math]m=3d; m=2d[/math]
  3. [math]m=3d; m+13=2(d+13)[/math]
  4. [math]m=3d; d+13=2(m+13)[/math]
9. 
Solve the following system for [math]x[/math].
[math]-4x-15y+17=0[/math]
[math]-x+5y+13=0[/math]
  1. 1
  2. 8
  3. -1
  4. -8
10. 
Write an equivalent system with integer coefficients.
[math]5x+(3/2)y=14[/math]
[math](5/6)x+5y=755/6[/math]
  1. [math]10x+3y=1; 5x+30y=1[/math]
  2. [math]10x+3y=28; 30x+5y=755[/math]
  3. [math]3x+10y=28; 5x+30y=755[/math]
  4. [math]10x+3y=28; 5x+30y=755[/math]
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