Solve the following pairs of equations by the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equations are:$(1) \ 9x + 7y = 55$$(2) \ 7x + 9y = 57$Adding equations $(1)$ and $(2)$:$(9x + 7x) + (7y + 9y) = 55 + 57$$16x + 16y = 112$Div

Vedclass · Accepted Answer

$(3, 4)$

Vedclass · Answer

(C) Given equations are:$(1) \ 9x + 7y = 55$$(2) \ 7x + 9y = 57$Adding equations $(1)$ and $(2)$:$(9x + 7x) + (7y + 9y) = 55 + 57$$16x + 16y = 112$Dividing by $16$:$x + y = 7 \quad (3)$Subtracting equation $(2)$ from $(1)$:$(9x - 7x) + (7y - 9y) = 55 - 57$$2x - 2y = -2$Dividing by $2$:$x - y = -1 \quad (4)$Adding equations $(3)$ and $(4)$:$(x + y) + (x - y) = 7 + (-1)$$2x = 6 \implies x = 3$Substituting $x = 3$ in equation $(3)$:$3 + y = 7 \implies y = 4$Thus,the solution is $(x, y) = (3, 4)$.

Solve the following pairs of equations by the method of elimination:
$9x + 7y = 55$
$7x + 9y = 57$

Similar Questions

If the sum of two numbers is $20$ and their difference is $8,$ then the larger number is ...........

Solve the following pairs of equations by the method of elimination:
$5(x-2) + 3y = 1$
$3(x+1) + 5(y-3) = 1$

Solve the following pair of linear equations: $\frac{9}{a} + \frac{8}{b} = 7$ and $\frac{2}{a} - \frac{3}{b} = -8$.

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{2}{a} = -1 - \frac{3}{b}$
$\frac{9}{b} = \frac{4}{a} + 7$

If $x=a$ and $y=b$ is the solution of the equations $x-y=2$ and $x+y=4,$ then the values of $a$ and $b$ are,respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Solve the following pairs of equations by the method of elimination:$9x + 7y = 55$$7x + 9y = 57$