Rewriting Equations To Use Substitution

What is the first step in solving the following system of equations?

 $3x+y=23$   $8x+2y=23$  

• Substitute the value of y from one equation into the other equation.

• Solve the first equation for y.

• Subtract the second equation from the first equation.

• Substitute the value of x from one equation into the other equation.

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CCSS.HSA.REI.A.1

CCSS.HSA.REI.C.6

Which shows the correct first step to solving the system of equations in the most efficient manner?

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CCSS.HSA.REI.C.5

CCSS.HSA.REI.C.6

In the system of equations, which variable would it be easiest to solve for?

• The easiest to solve for is x in the first equation.

• The easiest to solve for is y in the first equation.

• The easiest to solve for is x in the second equation.

• The easiest to solve for is y in the second equation.

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CCSS.HSA.REI.C.6

Malik solved this system of equations.

As the first step, he decided to solve for x in the first equation because it has a small, even number for the coefficient. Jill told him there was a more efficient way. What reason can Jill give for her statement?

• The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.

• The variable x in the second equation has a coefficient of 5 so it will be easy to divide 15 by 5.

• The variable y in the first equation is divisible by 2 so it will be the most efficient way to start.

• The variable y in the first equation has a larger even number. When dividing by 4, the solution will be a smaller number.

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CCSS.HSA.REI.A.1

CCSS.HSA.REI.C.6

Jerry solved the system of equations.

As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?

• The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.

• The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7.

• The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2.

• The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.

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CCSS.HSA.REI.A.1

CCSS.HSA.REI.C.6

In this system of equations, which variable would it be easiest to solve for?

• The easiest to solve for is x in the first equation.

• The easiest to solve for is y in the first equation.

• The easiest to solve for is x in the second equation.

• The easiest to solve for is y in the second equation.

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CCSS.HSA.REI.C.5

CCSS.HSA.REI.C.6

Theo solved the following problem correctly for homework.

What is the y-coordinate of his solution?

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Mr. Berger assigned the following system of equations to be solved for homework.

Which is the x-coordinate of the correct solution?

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CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

Herky was given the following system of equations to solve.

What is the solution to the system?

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CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What is the solution to the system of equations below?

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CCSS.HSA.REI.C.5

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11