Solve the system of equations: 2x + y = 3 and 4x − 2y = 4.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to solve the system of equations:

The given system of equations is:

2x + y = 3 \quad (1)

4x - 2y = 4 \quad (2)

Multiply equation (1) by 2 to make the coefficients of $y$ opposites.
$2(2x + y) = 2(3)$ $4x + 2y = 6 \quad (3)$
Add equation (3) to equation (2) to eliminate $y$ .
$(4x + 2y) + (4x - 2y) = 6 + 4$ $8x = 10$
Solve for $x$ .
$x = \frac{10}{8}$ $x = \frac{5}{4}$
Substitute the value of $x$ into equation (1) to solve for $y$ .
$2\left(\frac{5}{4}\right) + y = 3$ $\frac{10}{4} + y = 3$ $\frac{5}{2} + y = 3$ $y = 3 - \frac{5}{2}$ $y = \frac{6}{2} - \frac{5}{2}$ $y = \frac{1}{2}$
The solution to the system of equations is:
$x = \boxed{\frac{5}{4}}$ $y = \boxed{\frac{1}{2}}$

Answer