Answer:
x = 7 and y = 5.
Step-by-step explanation:
To solve the simultaneous equations:
1. 6x = 52 - 2y
2. 5x + 7y = 70
We'll first rearrange equation 1 to express x in terms of y, and then we'll substitute it into equation 2.
From equation 1:
6x = 52 - 2y
Divide both sides by 6:
[tex]x = \frac{52}{6} - \frac{2y}{6}\\\\x = \frac{26}{3} - \frac{y}{3}[/tex]
Now, substitute this expression for x into equation 2:
[tex]5\left(\frac{26}{3} - \frac{y}{3}\right) + 7y = 70[/tex]
Expand and solve for y:
[tex]5 \times \frac{26}{3} - 5 \times \frac{y}{3} + 7y = 70\\\\ \frac{130}{3} - \frac{5y}{3} + 7y = 70[/tex]
Multiply everything by 3 to get rid of the fractions:
130 - 5y + 21y = 210
Combine like terms:
130 + 16y = 210
Subtract 130 from both sides:
16y = 80
Divide both sides by 16:
y = 5
Now that we have y = 5, we can substitute it back into equation 1 to solve for x:
6x = 52 - 2(5)
6x = 52 - 10
6x = 42
[tex]x = \frac{42}{6}[/tex]
x = 7
