Linear Equation in Two Variables Quiz: Test Your Knowledge

  • CCSS.Math.Content.HSA-REI.C.6
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1) Solve for x: 5x - 2y = 10, x = 3, what is y?

Explanation

To solve 5x - 2y = 10, substitute x = 3 into the equation: 5(3) - 2y = 10, simplifying to 15 - 2y = 10.

Subtract 15 from both sides: -2y = -5. 
Divide both sides by -2 to get y = 5/2. 
Therefore, the value of y is 5/2 when x = 3.
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2) What is the solution for 2x + 3y = 12 and x - y = 2?

Explanation

To solve the system 2x + 3y = 12 and x - y = 2, first isolate x from the second equation: x = y + 2. 

Substitute x = y + 2 into the first equation: 2(y + 2) + 3y = 12. 
Simplifying, 2y + 4 + 3y = 12, which becomes 5y = 8. 
Therefore, y = 8/5. Substituting y = 8/5 back into x = y + 2 gives x = 8/5 + 2 = 18/5. 
Thus, the solution is x = 18/5 and y = 8/5.
Submit
3) If 3x + 5y = 20 and x = 2, what is the value of y?

Explanation

If 3x + 5y = 20 and x = 2, substitute x = 2 into the equation: 3(2) + 5y = 20, which simplifies to 6 + 5y = 20. 

Subtract 6 from both sides: 5y = 14. 
Divide by 5 to get y = 14/5. 
Therefore, the value of y is 14/5 when x = 2.
Submit
4) What is the solution to the system: x + y = 10 and 2x - y = 4?

Explanation

The system of equations is x + y = 10 and 2x - y = 4. 

Solve the first equation for y: y = 10 - x. 
Substitute this into the second equation: 2x - (10 - x) = 4, which simplifies to 2x - 10 + x = 4. Combining like terms: 3x - 10 = 4. Add 10 to both sides: 3x = 14. 
Dividing by 3 gives x = 14/3, and substituting into y = 10 - x gives y = 16/3.
Submit
5) What is the solution for 4x - y = 7 and x + y = 5?

Explanation

The system 4x - y = 7 and x + y = 5 can be solved by substitution. 

From the second equation, y = 5 - x. 
Substitute this into the first equation: 4x - (5 - x) = 7. 
Simplifying: 4x - 5 + x = 7, which becomes 5x - 5 = 7. 
Adding 5 to both sides gives 5x = 12. 
Divide by 5 to get x = 12/5. 
Substituting into y = 5 - x gives y = 13/5.
Submit
6) Solve for x: 7x + 2y = 21 and y = 2.

Explanation

Solve 7x + 2y = 21 and y = 2. 

Substitute y = 2 into the equation: 7x + 2(2) = 21, simplifying to 7x + 4 = 21. 
Subtract 4 from both sides: 7x = 17. 
Divide both sides by 7 to get x = 17/7. 
Thus, the value of x is 17/7 when y = 2.
Submit
7) If x + 2y = 10 and y = 3, what is x?

Explanation

If x + 2y = 10 and y = 3, substitute y = 3 into the equation: x + 2(3) = 10, simplifying to x + 6 = 10. Subtract 6 from both sides: x = 4. 

Thus, the value of x is 4 when y = 3.
Submit
8) What is the value of y when 2x + 3y = 12 and x = 4?

Explanation

The equation is 2x + 3y = 12 and x = 4. Substitute x = 4 into the equation: 2(4) + 3y = 12, simplifying to 8 + 3y = 12. 

Subtract 8 from both sides: 3y = 4. 
Divide by 3 to get y = 4/3. 
Therefore, the value of y is 4/3 when x = 4.
Submit
9) What is the solution for 2x + 5y = 25 and x = 3?

Explanation

For the equation 2x + 5y = 25 and x = 3, substitute x = 3 into the equation: 2(3) + 5y = 25, simplifying to 6 + 5y = 25. 

Subtract 6 from both sides: 5y = 19. 
Divide both sides by 5 to get y = 19/5. 
Therefore, the value of y is 19/5 when x = 3.
Submit
10) Solve for y in the equation: 3x + 4y = 12, if x = 2.

Explanation

Solve 3x + 4y = 12, given x = 2. 

Substitute x = 2 into the equation: 3(2) + 4y = 12, simplifying to 6 + 4y = 12. 
Subtract 6 from both sides: 4y = 6. 
Divide by 4 to get y = 6/4, which simplifies to y = 3/2. 
Thus, the value of y is 3/2 when x = 2.
Submit
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Solve for x: 5x - 2y = 10, x = 3, what is y?
What is the solution for 2x + 3y = 12 and x - y = 2?
If 3x + 5y = 20 and x = 2, what is the value of y?
What is the solution to the system: x + y = 10 and 2x - y = 4?
What is the solution for 4x - y = 7 and x + y = 5?
Solve for x: 7x + 2y = 21 and y = 2.
If x + 2y = 10 and y = 3, what is x?
What is the value of y when 2x + 3y = 12 and x = 4?
What is the solution for 2x + 5y = 25 and x = 3?
Solve for y in the equation: 3x + 4y = 12, if x = 2.
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