Question

Solve for x and y.
2x + 5y = 8
4x + 3y = 2
Ax = 2, y = -2
Bx = 1, y = 2
Cx = -1, y = 2
Dx = -2, y =
4

Answer 1

Answer:

C)  x = -1, y = 2

Step-by-step explanation:

Given system of linear equations:

$\begin{cases}2x + 5y = 8\\4x + 3y = 2\end{cases}$

Multiply the first equation by -2:

$\implies -2 \cdot 2x -2 \cdot 5y=-2 \cdot 8$

$\implies -4x-10y=-16$

Add this to the second equation to eliminate x:

$\begin{array}{crcrcr}& 4x & + & 3y & = & 2\\+&(-4x & - &10y&=&-16\\\cline{2-6}&&-&7y&=&-14\end{array}$

Solve for y:

$\implies -7y=-14$

$\implies \dfrac{-7y}{-7}=\dfrac{-14}{-7}$

$\implies y=2$

Substitute the found value of y into one of the equations and solve for x:

$\implies 2x+5(2)=8$

$\implies 2x+10=8$

$\implies 2x=-2$

$\implies x=-1$

Therefore the solution to the given system of linear equations is:

• x = -1, y = 2