Question

What is the y-value of the solution to the system of equations?

3x + 5y = 1
7x + 4y = -13
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Answer 1

{x = -3 , y=2 (Isolved for both variables be elimination)

Explanation:

Solve the following system:

{3 x + 5 y = 1 | (equation 1)

7 x + 4 y = -13 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 4 y = -13 | (equation 1)

3 x + 5 y = 1 | (equation 2)

Subtract 3/7 × (equation 1) from equation 2:

{7 x + 4 y = -13 | (equation 1)

0 x+(23 y)/7 = 46/7 | (equation 2)

Multiply equation 2 by 7/23:

{7 x + 4 y = -13 | (equation 1)

0 x+y = 2 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{7 x+0 y = -21 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 7:

{x+0 y = -3 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = -3 , y=2

Answer 2

y = 2

Explanation:

`\left\{\begin{array}{ccc}3x+5y=1&\text{multiply both sides by 7}\\7x+4y=-13&\text{multiply both sides by (-3)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}21x+35y=7\\-21x-12y=39\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad23y=46\qquad\text{divide both sides by 23}\\.\qquad\qquad y=2`

If you want to solve it to the end, put the value of y in the first equation and solve it for x.

3x + 5(2) = 1

3x + 10 = 1 subtract 10 from both sides

3x = -9 divide both sides by 3

x = -3