Grade 8 Math Algebra: Solving Systems of Equations

Answer explanation

To solve the system, substitute x from the second equation into the first: 2(1+y) + 3y = 12. Simplifying gives y = 2, then x = 3. Thus, the solution is x = 3, y = 2.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the system, substitute y from the second equation into the first: 3x - 2(4 - x) = 6. Simplifying gives 3x - 8 + 2x = 6, leading to 5x = 14, so x = 2. Then, y = 4 - 2 = 2. Thus, x = 2, y = 2 is correct.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the equations, substitute y from the first equation into the second. From x + 2y = 10, we get y = (10 - x)/2. Substituting into 2x - y = 3 gives x = 5 and y = 2, which matches the correct choice.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the system, substitute y from the first equation into the second. From 4x + y = 9, we get y = 9 - 4x. Substituting into 2x - 3(9 - 4x) = -6 leads to x = 2. Plugging x back gives y = 1. Thus, x = 2, y = 1 is correct.

Tags

CCSS.HSA.REI.C.9

Answer explanation

To solve the system, substitute y from the first equation into the second. From 5x - y = 7, we get y = 5x - 7. Substituting into 3x + 2(5x - 7) = 12 gives x = 2. Then, y = 1. Thus, the correct answer is x = 2, y = 1.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the system, substitute from the first equation: x = 4y - 2 into the second equation. This gives 3(4y - 2) + 2y = 10. Simplifying leads to y = 2, then substituting back gives x = 3. Thus, the solution is x = 3, y = 2.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the system, substitute x from the second equation into the first. This gives 2(5) + 5y = 20, leading to y = 2. Thus, the solution is x = 5 and y = 2, which matches the correct choice.

Tags

CCSS.HSA.REI.C.9

Answer explanation

To solve the system, substitute y from the first equation into the second: 2x - (7 - x) = 4. This simplifies to 3x = 11, giving x = 4. Substituting x back, y = 3. Thus, the correct values are x = 4, y = 3.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the system, substitute x from the second equation into the first. From x - 2y = -1, we get x = 2y - 1. Substituting into 3(2y - 1) + 4y = 18 gives y = 3. Then, x = 2. Thus, the solution is x = 2, y = 3.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Answer explanation

To solve the system, substitute from the first equation: x = 11 - 3y into the second equation. This gives 2(11 - 3y) - y = 1. Simplifying leads to y = 2, then substituting back gives x = 5. Thus, the solution is x = 5, y = 2.

Tags

CCSS.HSA.REI.C.9