In the system of equations below, what is the value of y? 4x + 3y = 25 2x + 3y = 17 — SAT

In the system of equations below, what is the value of $y$ ?

4x + 3y = 25

2x + 3y = 17

Answer: 3

The value of

y

3

Subtracting the second equation from the first equation gives

(4x + 3y) - (2x + 3y) = 25 - 17

, which simplifies to

2x = 8

. Dividing by 2 gives

x = 4

. Substituting

x = 4

into the second equation gives

2(4) + 3y = 17

, which simplifies to

8 + 3y = 17

. Subtracting 8 from both sides gives

3y = 9

, and dividing by 3 gives

y = 3

Subtract the second equation from the first equation to eliminate the

y

term.

2x = 8

Subtracting the equations eliminates

3y

since it is common to both equations, leaving a single variable equation.

Solve for

x

by dividing both sides of the equation by 2.

x = 4

Dividing isolates the variable

x

so we can find its numerical value.

Substitute

x = 4

into the second equation

2x + 3y = 17

and solve for

y

y = 3

Substituting the value of

x

leaves only the variable

y

, which can then be isolated and solved.

Solving systems of linear equations using elimination

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