Use elimination to solve the system of equations.

Ask by Bob Flynn. in the United States

Mar 25,2025

Question

Use elimination to solve the system of equations. $$ \begin{array}{l}13 x+14 y=59 \ 4 x+7 y=37\end{array} $$

UpStudy AI · Accepted Answer

1. Multiply the second equation by $$2$$ to align the coefficients of $$y$$:

$$
2(4x + 7y) = 2(37) \quad \Rightarrow \quad 8x + 14y = 74
$$

2. Write the first equation:

$$
13x + 14y = 59
$$

3. Subtract the first equation from the equation obtained in step 1 to eliminate $$y$$:

$$
(8x + 14y) - (13x + 14y) = 74 - 59 
$$
$$
8x - 13x = 15 \quad \Rightarrow \quad -5x = 15
$$

4. Solve for $$x$$:

$$
x = \frac{15}{-5} = -3
$$

5. Substitute $$x = -3$$ into one of the original equations (using the second equation):

$$
4(-3) + 7y = 37
$$
$$
-12 + 7y = 37
$$
$$
7y = 37 + 12 = 49
$$
$$
y = \frac{49}{7} = 7
$$

Final solution:

$$
x = -3, \quad y = 7
$$
$$ x = -3 $$ and $$ y = 7 $$.

Use elimination to solve the system of equations.