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PSAT Math : How to find the solution for a system of equations

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #34 : Whole Numbers

2x-y=2

x+y=4

What is the solution of for the two systems of equations?

Possible Answers:

x=2

x=0

x=9

x=1

x=3

Correct answer:

x=2

Explanation:

We first add both systems of equations.

Left Hand Side:

(2x-y)+(x+y)=3x

Right Hand Side:

2+4=6

Our resulting equation is:

3x=6

We divide both sides by 3.

Left Hand Side:

$\frac{3x}{3}=x$

Right Hand Side:

$\frac{6}{3}=2$

Our resulting equation is:

x=2

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Example Question #32 : Whole Numbers

4x+y=8

x+4y=17

What is the solution of for the two systems?

Possible Answers:

y=6

y=4

y=1

y=3

y=2

Correct answer:

y=4

Explanation:

We first multiply the second equation by 4.

So our resulting equation is:

$x\cdot4+4y\cdot4=17\cdot4$

4x+16y=68

Then we subtract the first equation from the second new equation.

Left Hand Side:

(4x+y)-(4x+16y)=-15y

Right Hand Side:

6-68=-60

Resulting Equation:

-15y=-60

We divide both sides by -15

Left Hand Side:

$\frac{-15y}{-15}=y$

Right Hand Side:

$\frac{-60}{-15}=4$

Our result is:

y=4

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Example Question #11 : How To Find The Solution For A System Of Equations

Find the solutions for the following set of equations:

13x+2y=11

-5x-y=-1

Possible Answers:

x=2

y=-7.5

x=3

y=-14

x=1

y=-1

x=1

y=-4

$x=\frac{9}{13}$

y=1

Correct answer:

x=3

y=-14

Explanation:

If we multiply both sides of our bottom equation by , we get -10x-2y=-2 . We can now add our two equations, and eliminate , leaving only one variable. When we add the equations, we get 3x=9 . Therefore, x=3 . Finally, we go back to either of our equations, and plug in x=3 so we can solve for .

13(3)+2y=11

39+2y=11

2y=-28

y=-14

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Example Question #191 : Systems Of Equations

Give the solution to the system of equations below.

4x-3y=11

2x+y=13

Possible Answers:

(6, 1)

(2, -1)

(4, -3)

(5, 3)

No solution

Correct answer:

(5, 3)

Explanation:

4x-3y=11

2x+y=13

Solve the second equation for , allowing us to solve using the substitution method.

2x+y=13

y=13-2x

Substitute for in the first equation, and solve for .

4x-3(13-2x)=11

4x-39+6x=11

10x-39=11

10x=50

x=5

Now, substitute for in either equation; we will choose the second. This allows us to solve for .

2x+y=13

$2\cdot 5+y=13$

10+y=13

y=3

Now we can write the solution in the notation (x,y) , or (5,3) .

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PSAT Math : How to find the solution for a system of equations

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #34 : Whole Numbers

Example Question #32 : Whole Numbers

Example Question #11 : How To Find The Solution For A System Of Equations

Example Question #191 : Systems Of Equations

All PSAT Math Resources

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