Question

HELP ASAP- NO LINKS AND NO JOKES

a student solved a system of equations as shown below

3x+2y=7
5x-4y=-3

which step in the solution contains the first error

A. Step 4

B. Step 6

C. step 2

D. Step 1

Answer 1

A

Explanation:

step 3 is correct

x = 1

in step 4 the student has substituted x = 1 into y instead of x, that is

3x + 2(1) = 7 ← Incorrect substitution

Should be

3(1) + 2y = 7

3 + 2y = 7 ( subtract 3 from both sides )

2y = 4 ( divide both sides by 2 )

y = 2

Answer 2

A. Step 4

Explanation:

Identifying the error

In step 4 the value of x is supposed to be substituted into the second equation however the value of x is instead substituted for y which is the first error made

Solving it correctly and explaining each step.

We have the two equations 3x + 2y = 7 and 5x - 4y = -3

It appears that the elimination method is being used as the first step consist of multiplying the first equation by 2 so that we have the two variables -4y and 4y which can cancel out in the next step so we are going to use the elimination method as well to solve it correctly.

What is the elimination method?

The elimination method is a method used to solve a system of equations. When you have two variables that have the same coefficient ( number before variable; x or y ) but different signs ( it works if they have the same too ) you can add the two equations eliminating one of the variables. Using this method will leave you with a singular variable in which you can solve

Solving it using the elimination method

Again we have the two equations 3x + 2y = 7 and 5x - 4y = -3

(step 1) Notice how the first equation has 2y which can be multiplied by 2 resulting in us getting 4y which is opposite of -4y. This sets us up exactly for using the elimination method.

Thus the first step would be too multiply the first equation by 2

3x + 2y = 7

x2

------------------

6x + 4y = 14

Now we have the two equations 6x + 4y = 14 and 5x - 4y = -3

(step 2)Our next step would be to add the two equations so that the variable y is eliminated

6x + 4y = 14

+ 5x - 4y = -3

--------------------

11x 0 = 11

We're left with 11x = 11

(step 3)Our next step would be to solve for x

11x = 11

==> divide both sides by 11

x = 1

(step 4) Now that we have defined one of are variables we plug it in into one of the equations and solve for the other, this is step 4.

5x - 4y = -3

==> plug in x = 1

5(1) - 4y = -3

(step 5)==> simplify

5 - 4y = -3

(step 6) ==> subtract 5 from both sides

-4y = -8

(step 7) ==> divide both sides by -4

y = 2

The real solution would be (1,2)