Convert 10 to a fraction with denominator 43, giving (430)/(43). Subtracting (364)/(43) gives 2x = (66)/(43). Dividing both sides by 2 yields x = (33)/(43).

$7y + 2x = 10$ $3y+7x=9$ Find x and y

Answer: $x = \frac{33}{43}, \quad y = \frac{52}{43}$

Step-by-step solution

Step 1: Multiply equations to align coefficients

We use the method of elimination to solve for the variables. To eliminate $x$ , multiply Equation (1) by 7 and Equation (2) by 2 so that both equations have the same coefficient, 14, for $x$ .

Step 2: Subtract the equations to solve for y

Subtract Equation (4) from Equation (3). The terms containing $x$ cancel out, leaving $43y = 52$ . Dividing both sides by 43 yields $y = \frac{52}{43}$ .

Step 3: Substitute y into Equation (1) to solve for x

Now substitute the value $y = \frac{52}{43}$ into the first equation, $2x + 7y = 10$ . Multiplying 7 by 52 gives 364, which gives $2x + \frac{364}{43} = 10$ .

Step 4: Isolate and solve for x

Convert 10 to a fraction with denominator 43, giving $\frac{430}{43}$ . Subtracting $\frac{364}{43}$ gives $2x = \frac{66}{43}$ . Dividing both sides by 2 yields $x = \frac{33}{43}$ .

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